【题文】已知log(2m-4)+log(n-4)=3,则的最小值为
【题文】已知log(2m-4)+log(n-4)=3,则的最小值为
题型:难度:来源:
【题文】已知log
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055045-86468.png)
(2m-4)+log
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055045-86468.png)
(n-4)=3,则
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055046-59866.png)
的最小值为
.
答案
【答案】
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055046-27829.png)
解析
【解析】
试题分析:由已知可得
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055046-70286.png)
,因为log
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055045-86468.png)
(2m-4)+ log
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055045-86468.png)
(n-4)=3,所以log
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055045-86468.png)
(2m-4)(n-4)=3,
即(2m-4)(n-4)=8,整理得
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055047-95261.png)
,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055046-59866.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055047-60847.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055047-54081.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055047-63286.png)
,当且仅当
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331055048-74096.png)
即n=6时,取等号.
考点:1.基本不等式;2.对数的运算性质.
举一反三
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331054727-49331.png)
的两个极值点分别为
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331054727-96833.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331054727-91470.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331054728-73493.png)
,点
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331054728-26017.png)
表示的平面区域为
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331054729-95056.png)
,若函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331054729-65723.png)
的图象上存在区域
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331054729-95056.png)
内的点,则实数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331054729-91142.png)
的取值范围为
.
【题文】当
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331054509-53642.png)
时,不等式
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331054509-92430.png)
恒成立,则实数a的取值范围为
.
【题文】求
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331054503-17992.png)
的值是
.
【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331053823-86116.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331053823-34083.png)
的大小关系是( )
【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331053724-28760.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331053725-74803.png)
的大小关系是( )
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