【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/20200328/20200328014310-40189.png)
log
85
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014310-46902.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/20200328/20200328014311-96388.png)
;(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014311-66420.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/20200328/20200328014310-40189.png)
log
85
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014310-46902.png)
log
2516 + log
324
=
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014311-63271.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014312-48703.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014312-93756.png)
=1
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014312-56956.png)
(2)由于底数为2,函数
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014313-69154.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014313-45621.png)
上是增函数,
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014313-97364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014314-71441.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014314-47595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014314-30688.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014315-95760.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/20200328/20200328014231-90159.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014231-86370.png)
的值;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014232-17922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014232-79992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014232-72758.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014233-31648.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014232-79992.png)
的值.
【题文】某彩电价格在去年6月份降价10%,后来经过10、11、12三个月连续三次涨价,回升到6月份降价前的水平,则这三次价格涨价的平均回升率是 ( )
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014201-32220.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014201-60570.png)
的值为( )
A.![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014202-34987.png) | B.4 | C.2 | D.![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014202-50569.png) |
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014138-11965.png)
的图象可能是( )
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328014139-73559.png)
【题文】已知
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328013932-35415.png)
,那么
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328013932-20327.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328013933-87903.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328013933-73091.png)
的大小关系为
(用
![](http://img.shitiku.com.cn/uploads/allimg/20200328/20200328013933-74973.png)
号表示)。
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