【题文】(本小题满分12分)(1)化简log85 log2516 + log324 .(2)若log2(3x-2)<2,试求x的取值范围.
题型:难度:来源:
【题文】(本小题满分12分)
(1)化简
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095831-59685.png)
log
85
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095831-53159.png)
log
2516 + log
324 .
(2)若log
2(3x-2)<2,试求x的取值范围.
答案
【答案】(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095832-12750.png)
;(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095833-73133.png)
解析
【解析】
试题分析:第一个小题是指数和对数运算,需要使用指数运算公式,对数运算公式,指数、对数运算法则及对数换底公式;第二个小题是解对数不等式,可用同底法去解,也可利用对数图象和性质去解,或直接运用指、对互化去解均可。
试题解析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095831-59685.png)
log
85
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095831-53159.png)
log
2516 + log
324
=
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095833-20978.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095833-32074.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095834-49280.png)
=1
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095834-66535.png)
(2)由于底数为2,函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095834-50255.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095835-86347.png)
上是增函数,
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095835-32835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095835-87925.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095836-76024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095836-27179.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095836-43208.png)
,故x的取值范围为
考点:1指数运算公式;2.指数运算法则;3.对数运算公式;4.对数运算法则;5.对数换底公式;5.解
对数不等式
举一反三
【题文】(本题满分14分)
(1)已知
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095820-23620.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095820-39418.png)
的值;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095820-12135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095821-88473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095821-26831.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095821-95211.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095821-88473.png)
的值.
【题文】(本题满分14分)
(1)已知
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095800-85946.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095801-24408.png)
的值;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095801-98218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095801-14306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095802-53609.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095802-92437.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095801-14306.png)
的值.
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095750-50665.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095750-58817.png)
的值为( )
A.![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095751-24285.png) | B.4 | C.2 | D.![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095751-53314.png) |
【题文】计算:
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095745-90014.png)
=____________.
【题文】已知
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095725-83122.png)
在区间
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095725-88115.png)
上为减函数,则实数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095726-47416.png)
的取值范围是____________.
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