![](https://wkrtcs.bdimg.com/rtcs/image?w=36.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_1","w":"36.00","h":"29.33","dataType":"png","c":"word/media/image1.png","imgOriW":27,"imgOriH":22})
秒杀高考数学题型之初等函数的应用（比较大小）
【秒杀题型一】：比较大小。
【题型1】：同底或同指（或可化简为同底与同指）比较大小。
『秒杀策略』：构造指 、对数及其它函数，利用增减性比较大小。
1.(2013年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=8.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"8.00","h":"30.67","dataType":"gif","c":"word/media/image2.gif"})
8)设，，。则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image6_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
2.(高考题)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=67.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"67.00","h":"21.00","dataType":"png","c":"word/media/image10_1.png","imgOriW":1763,"imgOriH":564})
，，,则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"wmf","c":"word/media/image13.png"})
B. C. D.
3.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=55.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"55.00","h":"25.00","dataType":"png","c":"word/media/image17_1.png","imgOriW":1312,"imgOriH":608})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=79.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"79.00","h":"24.00","dataType":"png","c":"word/media/image20_1.png","imgOriW":1888,"imgOriH":576})
B. C. D.
4.(高考题)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=79.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"79.00","h":"23.00","dataType":"wmf","c":"word/media/image24.png"})
，，，则 ( )
A. B. C. D.
5.(2016年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=10.67&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"10.67","h":"30.67","dataType":"gif","c":"word/media/image27.gif"})
6)已知，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image31_1.png","imgOriW":1587,"imgOriH":493})
B. C. D.
6.(高考题)若![](https://wkrtcs.bdimg.com/rtcs/image?w=83.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_14","w":"83.00","h":"21.00","dataType":"wmf","c":"word/media/image35.png"})
，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_14","w":"48.00","h":"21.00","dataType":"png","c":"word/media/image36_1.png","imgOriW":1152,"imgOriH":512})
B. C. D.
7.(高考题)已知实数![](https://wkrtcs.bdimg.com/rtcs/image?w=13.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"13.00","h":"15.00","dataType":"png","c":"word/media/image40_1.png","imgOriW":352,"imgOriH":388})
，满足，则下列关系式恒成立的是 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=49.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"49.00","h":"24.00","dataType":"png","c":"word/media/image43_1.png","imgOriW":1184,"imgOriH":576})
B. C. D.
8.(高考题)已知定义在R上的函数![](https://wkrtcs.bdimg.com/rtcs/image?w=104.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"104.00","h":"28.00","dataType":"png","c":"word/media/image47_1.png","imgOriW":2496,"imgOriH":672})
(为实数)为偶函数，记：，， ，则、、的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"wmf","c":"word/media/image55.png"})
B. C. D.
9.(高考母题)（1）已知![](https://wkrtcs.bdimg.com/rtcs/image?w=153.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"153.00","h":"51.00","dataType":"png","c":"word/media/image59_1.png","imgOriW":2358,"imgOriH":779})
求的值；
（2）已知![](https://wkrtcs.bdimg.com/rtcs/image?w=151.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"151.00","h":"51.00","dataType":"png","c":"word/media/image61_1.png","imgOriW":2336,"imgOriH":786})
求的值；
（3）比较![](https://wkrtcs.bdimg.com/rtcs/image?w=27.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"27.00","h":"21.00","dataType":"png","c":"word/media/image63_1.png","imgOriW":640,"imgOriH":512})
的大小.
10.(高考题)若![](https://wkrtcs.bdimg.com/rtcs/image?w=55.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"55.00","h":"41.00","dataType":"png","c":"word/media/image64_1.png","imgOriW":1446,"imgOriH":1093})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image67_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
11.(2017年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=4.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"4.00","h":"30.67","dataType":"gif","c":"word/media/image71.gif"})
11)设、、为正数，且，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=85.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"85.00","h":"21.00","dataType":"wmf","c":"word/media/image76.png"})
B. C. D.
12.(2020年新课标全国卷10)设，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_20","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image83_1.png","imgOriW":1587,"imgOriH":493})
B. C. D.
13.(2020年新课标全国卷12)已知，，设，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image92_1.png","imgOriW":1587,"imgOriH":493})
B. C. D.
【题型2】：不同底或不同指比较大小。
『秒杀策略』：先划分区间，一般划分为![](https://wkrtcs.bdimg.com/rtcs/image?w=51.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"51.00","h":"23.00","dataType":"png","c":"word/media/image96_1.png","imgOriW":1340,"imgOriH":599})
，，三个区间，若比较不出，再细化区间。
1.(2014年辽宁卷)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=49.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"49.00","h":"32.00","dataType":"wmf","c":"word/media/image99.png"})
,，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image101_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
2.(高考题)下列大小关系正确的是 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=132.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"132.00","h":"25.00","dataType":"png","c":"word/media/image105_1.png","imgOriW":3168,"imgOriH":608})
B.
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=131.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"131.00","h":"25.00","dataType":"png","c":"word/media/image107_1.png","imgOriW":3136,"imgOriH":608})
D.
3.(2019年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=4.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_7","w":"4.00","h":"30.67","dataType":"gif","c":"word/media/image71.gif"})
3)已知，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_9","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image112_1.png","imgOriW":1587,"imgOriH":493})
B. C. D.
4.(高考题)下面不等式成立的是 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=147.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_12","w":"147.00","h":"24.00","dataType":"png","c":"word/media/image116_1.png","imgOriW":3520,"imgOriH":576})
B.
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=152.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_12","w":"152.00","h":"24.00","dataType":"png","c":"word/media/image118_1.png","imgOriW":3313,"imgOriH":523})
D.
5.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=68.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"68.00","h":"23.00","dataType":"wmf","c":"word/media/image120.png"})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=69.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"69.00","h":"21.00","dataType":"png","c":"word/media/image123_1.png","imgOriW":1664,"imgOriH":512})
B. C. D.
6.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=69.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"69.00","h":"24.00","dataType":"png","c":"word/media/image127_1.png","imgOriW":1834,"imgOriH":635})
,,,则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"wmf","c":"word/media/image130.png"})
B. C. D.
7.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=68.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"68.00","h":"36.00","dataType":"png","c":"word/media/image134_1.png","imgOriW":1799,"imgOriH":952})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image137_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
8.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=67.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"67.00","h":"24.00","dataType":"wmf","c":"word/media/image141.png"})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image144_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
9.(高考题)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=55.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"55.00","h":"19.00","dataType":"png","c":"word/media/image148_1.png","imgOriW":1446,"imgOriH":493})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=64.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"64.00","h":"17.00","dataType":"wmf","c":"word/media/image151.png"})
B. C. D.
10.(2019年高考题天津卷)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=67.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_1","w":"67.00","h":"24.00","dataType":"png","c":"word/media/image155_1.png","imgOriW":1763,"imgOriH":635})
，，，则的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=53.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_1","w":"53.00","h":"17.00","dataType":"png","c":"word/media/image159_1.png","imgOriW":1280,"imgOriH":416})
B. C. D.
11.(2019年高考题天津卷)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=67.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_1","w":"67.00","h":"24.00","dataType":"wmf","c":"word/media/image163.png"})
，，，则的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_1","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image166_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
12.(高考题)若![](https://wkrtcs.bdimg.com/rtcs/image?w=49.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"49.00","h":"21.00","dataType":"png","c":"word/media/image167_1.png","imgOriW":1184,"imgOriH":512})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image170_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
13.(高考题)若![](https://wkrtcs.bdimg.com/rtcs/image?w=69.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"69.00","h":"24.00","dataType":"png","c":"word/media/image174_1.png","imgOriW":1834,"imgOriH":635})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image177_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
14.(高考题)三个数![](https://wkrtcs.bdimg.com/rtcs/image?w=25.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"25.00","h":"21.00","dataType":"png","c":"word/media/image181_1.png","imgOriW":670,"imgOriH":564})
，，的大小关系为 。
15.(2013年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=8.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"8.00","h":"30.67","dataType":"gif","c":"word/media/image2.gif"})
)设，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"18.00","dataType":"png","c":"word/media/image187_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
16.(2018年天津卷)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=67.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_9","w":"67.00","h":"23.00","dataType":"png","c":"word/media/image191_1.png","imgOriW":1763,"imgOriH":599})
，，，则、、的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_9","w":"60.00","h":"18.00","dataType":"wmf","c":"word/media/image197.png"})
B. C. D.
17.(高考题)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=49.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"49.00","h":"21.00","dataType":"png","c":"word/media/image201_1.png","imgOriW":1184,"imgOriH":512})
，，，则的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image205_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
18.(高考题)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=131.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"131.00","h":"27.00","dataType":"png","c":"word/media/image209_1.png","imgOriW":3136,"imgOriH":640})
，，，则、、的大小关系是
( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image212_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
19.(2020年高考题天津卷6)设![](https://wkrtcs.bdimg.com/rtcs/image?w=204.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_9","w":"204.00","h":"41.00","dataType":"png","c":"word/media/image216_1.png","imgOriW":3019,"imgOriH":612})
，则的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_9","w":"60.00","h":"19.00","dataType":"wmf","c":"word/media/image218.png"})
B. C. D.
20.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=51.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"51.00","h":"21.00","dataType":"png","c":"word/media/image222_1.png","imgOriW":1340,"imgOriH":564})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image225_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
21.(高考题)下列四个数中最大的是 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=44.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"44.00","h":"24.00","dataType":"wmf","c":"word/media/image229.png"})
B. C. D.
22.(高考题)若![](https://wkrtcs.bdimg.com/rtcs/image?w=64.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"64.00","h":"24.00","dataType":"png","c":"word/media/image233_1.png","imgOriW":1693,"imgOriH":635})
，，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image237_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
23.(2017年天津卷)已知奇函数![](https://wkrtcs.bdimg.com/rtcs/image?w=35.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"35.00","h":"23.00","dataType":"png","c":"word/media/image241_1.png","imgOriW":917,"imgOriH":599})
在R上是增函数，若，，，则、、的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"18.00","dataType":"png","c":"word/media/image245_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
24.(2019年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=10.67&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_5","w":"10.67","h":"30.67","dataType":"gif","c":"word/media/image27.gif"})
11)设是定义域为R的偶函数，且在单调递减，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=207.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"207.00","h":"51.00","dataType":"png","c":"word/media/image251_1.png","imgOriW":2762,"imgOriH":677})
B.
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=207.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"207.00","h":"51.00","dataType":"png","c":"word/media/image253_1.png","imgOriW":2762,"imgOriH":677})
D.
【题型3】：含字母比较大小。
『秒杀策略』：构造函数，利用函数的单调性与字母的范围比较大小，或划分区间比较大小。
秒杀方法：赋特值比较大小。
1.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=35.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"35.00","h":"19.00","dataType":"png","c":"word/media/image255_1.png","imgOriW":832,"imgOriH":448})
，且，，，则、、的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=68.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"68.00","h":"17.00","dataType":"png","c":"word/media/image262_1.png","imgOriW":1632,"imgOriH":416})
B. C. D.
2.(2016年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=4.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_4","w":"4.00","h":"30.67","dataType":"gif","c":"word/media/image71.gif"})
8)若，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"48.00","h":"21.00","dataType":"png","c":"word/media/image268_1.png","imgOriW":1152,"imgOriH":512})
B. C. D.
3.(高考题)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=61.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"61.00","h":"19.00","dataType":"png","c":"word/media/image272_1.png","imgOriW":1472,"imgOriH":448})
，令，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image276_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
4.(2021年模拟题精选)若![](https://wkrtcs.bdimg.com/rtcs/image?w=72.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_9","w":"72.00","h":"17.00","dataType":"wmf","c":"word/media/image280.png"})
，，，，则，，大小关系正确的
是 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=54.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_9","w":"54.00","h":"17.00","dataType":"png","c":"word/media/image287_1.png","imgOriW":1312,"imgOriH":416})
B. C. D.
5.(2021年模拟题精选)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=104.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"104.00","h":"19.00","dataType":"wmf","c":"word/media/image291.png"})
，则下列不等式不成立的是 ( )
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"48.00","h":"21.00","dataType":"wmf","c":"word/media/image292.png"})
B． C． D．
【题型4】：函数比较大小。
『秒杀策略』：在同一个坐标系中画出函数的图象，确定图象的交点，在相邻两个交点之间观察图象的高低，进而确定函数大小。
1.(2009年新课标全国卷12)用![](https://wkrtcs.bdimg.com/rtcs/image?w=76.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"76.00","h":"23.00","dataType":"wmf","c":"word/media/image296.png"})
表示三个数中的最小值，设
![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"48.00","h":"21.00","dataType":"png","c":"word/media/image299_1.png","imgOriW":1270,"imgOriH":564})
，则的最大值为 ( )
A.4 B.5 C.6 D.7
![](https://wkrtcs.bdimg.com/rtcs/image?w=161.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_12","w":"161.00","h":"146.00","dataType":"jpeg","c":"word/media/image301.jpeg","imgOriW":369,"imgOriH":335})
![](https://wkrtcs.bdimg.com/rtcs/image?w=49.33&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_15","w":"49.33","h":"52.00","dataType":"png","c":"word/media/image302.png","imgOriW":37,"imgOriH":39})
秒杀高考数学题型之初等函数的应用（比较大小）
【秒杀题型一】：比较大小。
【题型1】：同底或同指（或可化简为同底与同指）比较大小。
『秒杀策略』：构造指 、对数及其它函数，利用增减性比较大小。
1.(2013年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=8.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_4","w":"8.00","h":"30.67","dataType":"gif","c":"word/media/image2.gif"})
8)设，，。则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image6_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：法一：可化简为同底对数型：![](https://wkrtcs.bdimg.com/rtcs/image?w=179.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_20","w":"179.00","h":"44.00","dataType":"png","c":"word/media/image303_1.png","imgOriW":2774,"imgOriH":674})
，=，
![](https://wkrtcs.bdimg.com/rtcs/image?w=72.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_20","w":"72.00","h":"24.00","dataType":"wmf","c":"word/media/image305.png"})
=，选D。
法二：构造函数![](https://wkrtcs.bdimg.com/rtcs/image?w=247.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_20","w":"247.00","h":"45.00","dataType":"png","c":"word/media/image307_1.png","imgOriW":3212,"imgOriH":590})
，为减函数，选D。
2.(高考题)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=67.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_4","w":"67.00","h":"21.00","dataType":"png","c":"word/media/image10_1.png","imgOriW":1763,"imgOriH":564})
，，,则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"60.00","h":"19.00","dataType":"wmf","c":"word/media/image13.png"})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=67.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_20","w":"67.00","h":"21.00","dataType":"png","c":"word/media/image10_1.png","imgOriW":1763,"imgOriH":564})
，，，，选C。
3.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=55.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"55.00","h":"25.00","dataType":"png","c":"word/media/image17_1.png","imgOriW":1312,"imgOriH":608})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=79.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"79.00","h":"24.00","dataType":"png","c":"word/media/image20_1.png","imgOriW":1888,"imgOriH":576})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=92.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"92.00","h":"24.00","dataType":"png","c":"word/media/image312_1.png","imgOriW":2434,"imgOriH":635})
，，，选D。
4.(高考题)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=79.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"79.00","h":"23.00","dataType":"wmf","c":"word/media/image24.png"})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"19.00","dataType":"wmf","c":"word/media/image13.png"})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=125.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"125.00","h":"24.00","dataType":"png","c":"word/media/image315_1.png","imgOriW":3009,"imgOriH":576})
，选B。
5.(2016年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=10.67&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_11","w":"10.67","h":"30.67","dataType":"gif","c":"word/media/image27.gif"})
6)已知，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image31_1.png","imgOriW":1587,"imgOriH":493})
B. C. D.
【解析】：由指数函数的单调性得![](https://wkrtcs.bdimg.com/rtcs/image?w=109.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"109.00","h":"32.00","dataType":"wmf","c":"word/media/image316.png"})
，由幂函数的单调性得，选A。
6.(高考题)若![](https://wkrtcs.bdimg.com/rtcs/image?w=83.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_12","w":"83.00","h":"21.00","dataType":"wmf","c":"word/media/image35.png"})
，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_12","w":"48.00","h":"21.00","dataType":"png","c":"word/media/image36_1.png","imgOriW":1152,"imgOriH":512})
B. C. D.
【解析】：选C。
7.(高考题)已知实数![](https://wkrtcs.bdimg.com/rtcs/image?w=13.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"13.00","h":"15.00","dataType":"png","c":"word/media/image40_1.png","imgOriW":352,"imgOriH":388})
，满足，则下列关系式恒成立的是 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=49.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"49.00","h":"24.00","dataType":"png","c":"word/media/image43_1.png","imgOriW":1184,"imgOriH":576})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=51.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"51.00","h":"17.00","dataType":"png","c":"word/media/image318_1.png","imgOriW":1340,"imgOriH":458})
，而为增函数，所以选A。
8.(高考题)已知定义在R上的函数![](https://wkrtcs.bdimg.com/rtcs/image?w=104.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"104.00","h":"28.00","dataType":"png","c":"word/media/image47_1.png","imgOriW":2496,"imgOriH":672})
(为实数)为偶函数，记：，， ，则、、的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"19.00","dataType":"wmf","c":"word/media/image55.png"})
B. C. D.
【解析】：由![](https://wkrtcs.bdimg.com/rtcs/image?w=36.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"36.00","h":"21.00","dataType":"png","c":"word/media/image320_1.png","imgOriW":952,"imgOriH":564})
是偶函数得，所以选减后增，，，因为
![](https://wkrtcs.bdimg.com/rtcs/image?w=119.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"119.00","h":"23.00","dataType":"png","c":"word/media/image325_1.png","imgOriW":3139,"imgOriH":599})
，所以选C。
9.(高考母题)（1）已知![](https://wkrtcs.bdimg.com/rtcs/image?w=153.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"153.00","h":"51.00","dataType":"png","c":"word/media/image59_1.png","imgOriW":2358,"imgOriH":779})
求的值；
（2）已知![](https://wkrtcs.bdimg.com/rtcs/image?w=151.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"151.00","h":"51.00","dataType":"png","c":"word/media/image61_1.png","imgOriW":2336,"imgOriH":786})
求的值；
（3）比较![](https://wkrtcs.bdimg.com/rtcs/image?w=27.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"27.00","h":"21.00","dataType":"png","c":"word/media/image63_1.png","imgOriW":640,"imgOriH":512})
的大小.
【解析】：（1）![](https://wkrtcs.bdimg.com/rtcs/image?w=49.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"49.00","h":"23.00","dataType":"wmf","c":"word/media/image326.png"})
; （2); （3）。
10.(高考题)若![](https://wkrtcs.bdimg.com/rtcs/image?w=55.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"55.00","h":"41.00","dataType":"png","c":"word/media/image64_1.png","imgOriW":1446,"imgOriH":1093})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image67_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：法一：两两比较：![](https://wkrtcs.bdimg.com/rtcs/image?w=116.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"116.00","h":"41.00","dataType":"png","c":"word/media/image330_1.png","imgOriW":2232,"imgOriH":795})
，，，只需比较的大小，化为根指数相同即：；；，可得答案C。
法二：构造函数![](https://wkrtcs.bdimg.com/rtcs/image?w=31.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"31.00","h":"41.00","dataType":"wmf","c":"word/media/image337.png"})
，求导可知单调区间为：当时，单调递减，而，即。
11.(2017年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=4.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_11","w":"4.00","h":"30.67","dataType":"gif","c":"word/media/image71.gif"})
11)设、、为正数，且，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=85.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"85.00","h":"21.00","dataType":"wmf","c":"word/media/image76.png"})
B. C. D.
【解析】：设![](https://wkrtcs.bdimg.com/rtcs/image?w=103.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"103.00","h":"21.00","dataType":"png","c":"word/media/image341_1.png","imgOriW":2716,"imgOriH":564})
，则，，，
![](https://wkrtcs.bdimg.com/rtcs/image?w=216.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"216.00","h":"61.00","dataType":"png","c":"word/media/image346_1.png","imgOriW":2595,"imgOriH":736})
，同理：，，转化为比较的大小，仿照上题的两种解法，选D。
12.(2020年新课标全国卷10)设，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_18","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image83_1.png","imgOriW":1587,"imgOriH":493})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=136.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"136.00","h":"44.00","dataType":"png","c":"word/media/image350_1.png","imgOriW":2378,"imgOriH":769})
，等价于比较2与、3与的大小，即与、与的大小，选A。
13.(2020年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=10.67&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"10.67","h":"30.67","dataType":"gif","c":"word/media/image27.gif"})
12)已知，，设，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_4","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image92_1.png","imgOriW":1587,"imgOriH":493})
B. C. D.
【解析】：可知![](https://wkrtcs.bdimg.com/rtcs/image?w=81.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"81.00","h":"23.00","dataType":"wmf","c":"word/media/image357.png"})
，从已知条件可确定与比较大小，，即3与比较大小，等价于比较大小，，即，同理，，即比较与，即，，
因为![](https://wkrtcs.bdimg.com/rtcs/image?w=53.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"53.00","h":"21.00","dataType":"png","c":"word/media/image88_1.png","imgOriW":1411,"imgOriH":564})
，，而，，即，选A。
【题型2】：不同底或不同指比较大小。
『秒杀策略』：先划分区间，一般划分为![](https://wkrtcs.bdimg.com/rtcs/image?w=51.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_13","w":"51.00","h":"23.00","dataType":"png","c":"word/media/image96_1.png","imgOriW":1340,"imgOriH":599})
，，三个区间，若比较不出，再细化区间。
1.(2014年辽宁卷)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=49.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_4","w":"49.00","h":"32.00","dataType":"wmf","c":"word/media/image99.png"})
,，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_4","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image101_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=49.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"49.00","h":"32.00","dataType":"wmf","c":"word/media/image99.png"})
，，，选C。
2.(高考题)下列大小关系正确的是 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=132.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_17","w":"132.00","h":"25.00","dataType":"png","c":"word/media/image105_1.png","imgOriW":3168,"imgOriH":608})
B.
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=131.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_17","w":"131.00","h":"25.00","dataType":"png","c":"word/media/image107_1.png","imgOriW":3136,"imgOriH":608})
D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=77.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"77.00","h":"23.00","dataType":"png","c":"word/media/image376_1.png","imgOriW":2046,"imgOriH":599})
，，，选C。
3.(2019年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=4.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_1","w":"4.00","h":"30.67","dataType":"gif","c":"word/media/image71.gif"})
3)已知，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_16","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image112_1.png","imgOriW":1587,"imgOriH":493})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=37.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"37.00","h":"19.00","dataType":"wmf","c":"word/media/image379.png"})
，，，选B。
4.(高考题)下面不等式成立的是 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=147.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_19","w":"147.00","h":"24.00","dataType":"png","c":"word/media/image116_1.png","imgOriW":3520,"imgOriH":576})
B.
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=152.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_19","w":"152.00","h":"24.00","dataType":"png","c":"word/media/image118_1.png","imgOriW":3313,"imgOriH":523})
D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=192.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"192.00","h":"24.00","dataType":"png","c":"word/media/image382_1.png","imgOriW":3790,"imgOriH":474})
，选A。
5.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=68.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_17","w":"68.00","h":"23.00","dataType":"wmf","c":"word/media/image120.png"})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=69.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_17","w":"69.00","h":"21.00","dataType":"png","c":"word/media/image123_1.png","imgOriW":1664,"imgOriH":512})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=229.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"229.00","h":"24.00","dataType":"png","c":"word/media/image383_1.png","imgOriW":4169,"imgOriH":436})
，选A。
6.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=69.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_17","w":"69.00","h":"24.00","dataType":"png","c":"word/media/image127_1.png","imgOriW":1834,"imgOriH":635})
,,,则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_17","w":"60.00","h":"19.00","dataType":"wmf","c":"word/media/image130.png"})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=196.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"196.00","h":"27.00","dataType":"png","c":"word/media/image384_1.png","imgOriW":3651,"imgOriH":496})
，选A。
7.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=68.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_17","w":"68.00","h":"36.00","dataType":"png","c":"word/media/image134_1.png","imgOriW":1799,"imgOriH":952})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_17","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image137_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=304.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"304.00","h":"36.00","dataType":"png","c":"word/media/image385_1.png","imgOriW":4000,"imgOriH":473})
，选D。
8.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=67.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_17","w":"67.00","h":"24.00","dataType":"wmf","c":"word/media/image141.png"})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_17","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image144_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=235.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"235.00","h":"27.00","dataType":"png","c":"word/media/image386_1.png","imgOriW":4019,"imgOriH":456})
，选D。
9.(高考题)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=55.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_17","w":"55.00","h":"19.00","dataType":"png","c":"word/media/image148_1.png","imgOriW":1446,"imgOriH":493})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=64.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_17","w":"64.00","h":"17.00","dataType":"wmf","c":"word/media/image151.png"})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=168.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_8","w":"168.00","h":"44.00","dataType":"png","c":"word/media/image387_1.png","imgOriW":2661,"imgOriH":697})
，选D。
10.(2019年高考题天津卷)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=67.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"67.00","h":"24.00","dataType":"png","c":"word/media/image155_1.png","imgOriW":1763,"imgOriH":635})
，，，则的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=53.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"53.00","h":"17.00","dataType":"png","c":"word/media/image159_1.png","imgOriW":1280,"imgOriH":416})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=388.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"388.00","h":"41.00","dataType":"png","c":"word/media/image388_1.png","imgOriW":4254,"imgOriH":453})
，选A。
11.(2019年高考题天津卷)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=67.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"67.00","h":"24.00","dataType":"wmf","c":"word/media/image163.png"})
，，，则的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_2","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image166_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=187.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"187.00","h":"25.00","dataType":"wmf","c":"word/media/image389.png"})
，选A。
12.(高考题)若，，，则 ( )
A. B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"48.00","h":"20.00","dataType":"wmf","c":"word/media/image390.png"})
，，，选A。
13.(高考题)若，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image177_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=65.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"65.00","h":"24.00","dataType":"png","c":"word/media/image393_1.png","imgOriW":1728,"imgOriH":635})
，，，选A。
14.(高考题)三个数![](https://wkrtcs.bdimg.com/rtcs/image?w=25.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"25.00","h":"21.00","dataType":"png","c":"word/media/image181_1.png","imgOriW":670,"imgOriH":564})
，，的大小关系为 。
【解析】：分区间：![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"48.00","h":"21.00","dataType":"png","c":"word/media/image396_1.png","imgOriW":1152,"imgOriH":512})
，，，得。
15.(2013年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=8.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_13","w":"8.00","h":"30.67","dataType":"gif","c":"word/media/image2.gif"})
)设，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"18.00","dataType":"png","c":"word/media/image187_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=139.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"139.00","h":"45.00","dataType":"png","c":"word/media/image400_1.png","imgOriW":2369,"imgOriH":774})
，，且，，选D。
16.(2018年天津卷)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=67.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_14","w":"67.00","h":"23.00","dataType":"png","c":"word/media/image191_1.png","imgOriW":1763,"imgOriH":599})
，，，则、、的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_14","w":"60.00","h":"18.00","dataType":"wmf","c":"word/media/image197.png"})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=220.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"220.00","h":"45.00","dataType":"wmf","c":"word/media/image404.png"})
，，选D。
17.(高考题)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=49.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"49.00","h":"21.00","dataType":"png","c":"word/media/image201_1.png","imgOriW":1184,"imgOriH":512})
，，，则的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image205_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=195.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"195.00","h":"49.00","dataType":"png","c":"word/media/image406_1.png","imgOriW":2725,"imgOriH":690})
，，选A。
18.(高考题)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=131.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"131.00","h":"27.00","dataType":"png","c":"word/media/image209_1.png","imgOriW":3136,"imgOriH":640})
，，，则、、的大小关系是
( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image212_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=85.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"85.00","h":"25.00","dataType":"png","c":"word/media/image408_1.png","imgOriW":2257,"imgOriH":670})
，，，，选B。
19.(2020年高考题天津卷6)设![](https://wkrtcs.bdimg.com/rtcs/image?w=204.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_14","w":"204.00","h":"41.00","dataType":"png","c":"word/media/image216_1.png","imgOriW":3019,"imgOriH":612})
，则的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_14","w":"60.00","h":"19.00","dataType":"wmf","c":"word/media/image218.png"})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"48.00","h":"21.00","dataType":"png","c":"word/media/image412_1.png","imgOriW":1270,"imgOriH":564})
,，选D。
20.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=51.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"51.00","h":"21.00","dataType":"png","c":"word/media/image222_1.png","imgOriW":1340,"imgOriH":564})
，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image225_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：可知![](https://wkrtcs.bdimg.com/rtcs/image?w=77.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"77.00","h":"41.00","dataType":"wmf","c":"word/media/image414.png"})
，，，选B。
21.(高考题)下列四个数中最大的是 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=44.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_10","w":"44.00","h":"24.00","dataType":"wmf","c":"word/media/image229.png"})
B. C. D.
【解析】：可知![](https://wkrtcs.bdimg.com/rtcs/image?w=72.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"72.00","h":"19.00","dataType":"png","c":"word/media/image417_1.png","imgOriW":1905,"imgOriH":493})
，，，，选D。
22.(高考题)若![](https://wkrtcs.bdimg.com/rtcs/image?w=64.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"64.00","h":"24.00","dataType":"png","c":"word/media/image233_1.png","imgOriW":1693,"imgOriH":635})
，，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image237_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：可知![](https://wkrtcs.bdimg.com/rtcs/image?w=83.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"83.00","h":"19.00","dataType":"png","c":"word/media/image421_1.png","imgOriW":2187,"imgOriH":493})
，，，选C。
23.(2017年天津卷)已知奇函数![](https://wkrtcs.bdimg.com/rtcs/image?w=35.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"35.00","h":"23.00","dataType":"png","c":"word/media/image241_1.png","imgOriW":917,"imgOriH":599})
在R上是增函数，若，，，则、、的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"60.00","h":"18.00","dataType":"png","c":"word/media/image245_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=176.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"176.00","h":"41.00","dataType":"wmf","c":"word/media/image424.png"})
，因为，所以选C。
24.(2019年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=10.67&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_4","w":"10.67","h":"30.67","dataType":"gif","c":"word/media/image27.gif"})
11)设是定义域为R的偶函数，且在单调递减，则 ( )
A. B.
C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=163.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_12","w":"163.00","h":"36.00","dataType":"wmf","c":"word/media/image426.png"})
，选C。
【题型3】：含字母比较大小。
『秒杀策略』：构造函数，利用函数的单调性与字母的范围比较大小，或划分区间比较大小。
秒杀方法：赋特值比较大小。
1.(高考题)设![](https://wkrtcs.bdimg.com/rtcs/image?w=35.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"35.00","h":"19.00","dataType":"png","c":"word/media/image255_1.png","imgOriW":832,"imgOriH":448})
，且，，，则、、的大小关系为 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=68.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"68.00","h":"17.00","dataType":"png","c":"word/media/image262_1.png","imgOriW":1632,"imgOriH":416})
B. C. D.
【解析】：令![](https://wkrtcs.bdimg.com/rtcs/image?w=37.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"37.00","h":"19.00","dataType":"png","c":"word/media/image427_1.png","imgOriW":987,"imgOriH":493})
，则，，，选B。
2.(2016年新课标全国卷![](https://wkrtcs.bdimg.com/rtcs/image?w=4.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_14","w":"4.00","h":"30.67","dataType":"gif","c":"word/media/image71.gif"})
8)若，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"48.00","h":"21.00","dataType":"png","c":"word/media/image268_1.png","imgOriW":1152,"imgOriH":512})
B. C. D.
【解析】：A选项：构造幂函数![](https://wkrtcs.bdimg.com/rtcs/image?w=44.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"44.00","h":"24.00","dataType":"png","c":"word/media/image431_1.png","imgOriW":1164,"imgOriH":635})
，为增函数; B选项：构造幂函数，为减函数，,
![](https://wkrtcs.bdimg.com/rtcs/image?w=56.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"56.00","h":"44.00","dataType":"wmf","c":"word/media/image434.png"})
，即; D选项：构造函数，为减函数，即; C选项:,
![](https://wkrtcs.bdimg.com/rtcs/image?w=141.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"141.00","h":"24.00","dataType":"png","c":"word/media/image439_1.png","imgOriW":3212,"imgOriH":546})
，由乘法单调性可知，选C。
秒杀方法：![](https://wkrtcs.bdimg.com/rtcs/image?w=115.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"115.00","h":"41.00","dataType":"png","c":"word/media/image440_1.png","imgOriW":2235,"imgOriH":805})
，选C。
3.(高考题)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=61.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"61.00","h":"19.00","dataType":"png","c":"word/media/image272_1.png","imgOriW":1472,"imgOriH":448})
，令，，，则 ( )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=60.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"60.00","h":"19.00","dataType":"png","c":"word/media/image276_1.png","imgOriW":1440,"imgOriH":448})
B. C. D.
【解析】：![](https://wkrtcs.bdimg.com/rtcs/image?w=15.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"15.00","h":"13.00","dataType":"png","c":"word/media/image441_1.png","imgOriW":388,"imgOriH":352})
，，选D。
秒杀方法：令![](https://wkrtcs.bdimg.com/rtcs/image?w=39.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_3","w":"39.00","h":"19.00","dataType":"png","c":"word/media/image444_1.png","imgOriW":1023,"imgOriH":493})
，，，，，选D。
4.(2021年模拟题精选)若，，，，则，，大小关系正确的
是 ( )
A. B. C. D.
【解析】：取特殊值，令![](https://wkrtcs.bdimg.com/rtcs/image?w=36.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_19","w":"36.00","h":"37.00","dataType":"png","c":"word/media/image449_1.png","imgOriW":864,"imgOriH":896})
，，则，，，
则![](https://wkrtcs.bdimg.com/rtcs/image?w=80.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_19","w":"80.00","h":"51.00","dataType":"png","c":"word/media/image454_1.png","imgOriW":1662,"imgOriH":1053})
，即，可排除A、C、D选项，选B。
5.(2021年模拟题精选)已知![](https://wkrtcs.bdimg.com/rtcs/image?w=104.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_6","w":"104.00","h":"19.00","dataType":"wmf","c":"word/media/image291.png"})
，则下列不等式不成立的是 ( )
A．![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_5","w":"48.00","h":"21.00","dataType":"wmf","c":"word/media/image292.png"})
B． C． D．
【解析】：取![](https://wkrtcs.bdimg.com/rtcs/image?w=40.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_1","w":"40.00","h":"41.00","dataType":"wmf","c":"word/media/image456.png"})
，，，选项A：，成立。选项B：，不成立。选项C：，，，成立。选项D：，，，成立，选B。
【题型4】：函数比较大小。
『秒杀策略』：在同一个坐标系中画出函数的图象，确定图象的交点，在相邻两个交点之间观察图象的高低，进而确定函数大小。
1.(2009年新课标全国卷12)用![](https://wkrtcs.bdimg.com/rtcs/image?w=76.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_5","w":"76.00","h":"23.00","dataType":"wmf","c":"word/media/image296.png"})
表示三个数中的最小值，设
![](https://wkrtcs.bdimg.com/rtcs/image?w=48.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_5","w":"48.00","h":"21.00","dataType":"png","c":"word/media/image299_1.png","imgOriW":1270,"imgOriH":564})
，则的最大值为 ( )
A.4 B.5 C.6 D.7
【解析】：从图观察可知实线部分对应图象为![](https://wkrtcs.bdimg.com/rtcs/image?w=36.00&md5sum=a1ac7faf7583970034d763b67da8223d&sign=727816706c&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=574&ipr={"t":"img","r":"r_9","w":"36.00","h":"21.00","dataType":"wmf","c":"word/media/image467.png"})
的图象，其最高点为，选C。
