题目
题型:解答题难度:简单来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182450-76151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182450-90349.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182450-90661.png)
(2)x1、x2、…x2010均为正实数,若函数f(x)=logax(a>0且a≠1)且f(x1x2…x2010)=
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182450-90661.png)
求f(
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182450-26581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182451-31626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182451-40946.png)
答案
解析
(1)由100m=5,10n=2,知2m=lg5,n=lg2,由此能求出2m+n的值.
(2)由(1)知f(x1x2…x10)=f(x1)+f(x2)+…+f(x10)=1,由此能求出f(x12)+f(x22)+…+f(x102)的值.
析:(1)方法一:
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182451-55816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182451-47405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182451-28169.png)
方法二:
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182452-35016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182452-25633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182452-93549.png)
(2)由(1)可知f(x1x2…x2010)=f(x1)+f(x2)+…+f(2010)=1,……… 7分
∴f(
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182450-26581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182451-31626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182451-40946.png)
=2×1=2. ……… 10分
核心考点
试题【知,,(1)求的值.(2)x1、x2、…x2010均为正实数,若函数f(x)=logax(a>0且a≠1)且f(x1x2…x2010)=,求f()+f()+…+】;主要考察你对指数函数图象及性质等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182442-26741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182442-75836.png)
(1)试讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182442-23431.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182442-23431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182442-48823.png)
试证明:函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182443-92363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182443-66794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182443-13199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182437-19714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182438-12014.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182438-31239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182438-18913.png)
(1)证明:f(0)=1且x<0时f(x)>1;
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182426-86765.png)
(1)求关于x的方程
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182426-75179.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182426-52269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182427-61491.png)
(3)若关于x的方程
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182427-54728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182427-24194.png)
A.(2,3) | B.(1,2) | C.(0,1) | D.(-1,0) |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182418-18082.png)
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