1 . 对数函数
,
,
(
,
,
,且a,b,c均不为1)的图象如图,试比较a,b,c的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65cb3db3da689e6cad7cfc03048fcce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c276d040efa47145641c12fb89dc9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
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解题方法
2 . 已知下列不等式成立,比较正数m,n的大小:
(1)
;
(2)
;
(3)
(
,且
).
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5e627fd620a1c8a0b0fb8aaea21adf.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4048bd0c99412b0928e96e227dc3cf01.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1ee639114bb30095eeb425a88ebbaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
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3 . 比较下列各题中两个数的大小:
(1)
,
;
(2)
,
;
(3)
,
;
(4)
,
(
,且
,
).
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3a844d118337b249319df9f677ff68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f30787ec695c8ada488e61933e9b3c.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e234d52b17f7566f540442a9dde5bfe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e14615b567e97fb344054e087783bac.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8249d4825c18ee5dfbdce5c93800598c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39f5f72ceb7ea766e9be5ceb2f08d5f.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ccbca6a8542fc73c25a02a864cd3f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/922356464de580fafd1690c579e879bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66eba129d92ede31b728e2590c4db2a1.png)
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4 . 求下列函数的定义域:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9457936782dd115bd8f5ee4f7b89ad03.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4778a8f3aeb6a0715e570e198af61d07.png)
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5 . (1)计算对数函数
当
,3,9时的函数值;
(2)计算常用对数函数
当
,0.001,1000时的函数值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2702a5539ca829b8b7a08407f0996e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)计算常用对数函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f0fadbe551b0e0eb7bf9440be740b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad332186163dfc5b0f04ebaa32bc05.png)
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6 . 写出下列对数函数的反函数(用x表示自变量,用y表示函数):
(1)
;
(2)
;
(3)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2702a5539ca829b8b7a08407f0996e8a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3775a629bb29e890fd37692f5a6cf71.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4a90955ae3a90343d164a91e5f835c.png)
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7 . 当
,且
时,常用对数
和自然对数
可以互相转换,即存在实数A,使得
.你能推导出A的值吗?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a891d21bb2c7a11304beaab5054074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d582a8ea1d1846b22372ea56f6e44783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ccb245042079bba161c53d431a9160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f75a1642a5a899bf4a2c7e13a91273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57f9b2e089c13cfe604500815634606.png)
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8 . 利用对数的换底公式计算:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ff22f92d58ed85b08d25d9f4d3aec6.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86764bc88cfc2aeec69d560d10ba42c9.png)
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9 . 已知a,b是方程
的两个实数根,求下列各式的值:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b632669adb8f2859f1335aedb63512a6.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04af04d6a45fd724ad8b8de78b615965.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c9cd9d577c47efbdcefd03d71792be.png)
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10 . 求下列各式中x的值:
(1)
;
(2)
;
(3)
;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cac86bbb31ee7d9ecaaf30b3a030b40.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a490d8054f7f0342d5e79da8d9ba568.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9f6031400e6f0608f9b7c4a3eff788.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a95aeea8a9a747c198e5c1772287a2d.png)
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