1 . 设
,
,
.令
,
.
(1)请分别化简下列各式:①
;②
;③
;
(2)结合(1)中的化简结果,谈谈你对对数函数
、幂函数
、指数函数
变化的感受.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa1dac89223951cb5e627c1aa8b6e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419f8e2e08693764ea744ac6808f6e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cbe1fc2baa603805f02b5f5bf469d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3713297f235ddbdc65cb74baacd6668e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3493414b77a526ca286d225db3bb1dc.png)
(1)请分别化简下列各式:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef52060d97bafb43d8a53cfd21367b19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6111db3c756dcd21724dee3dbc5e071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b0f34948571b3b1efed8d5ae874fb2.png)
(2)结合(1)中的化简结果,谈谈你对对数函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9314bd1d7a6e070f4f2428f9a321804e.png)
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解题方法
2 . 设
,求满足
的x值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54ad27760b324ddeeaa5f842784e5f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1656a75d215f8c6d703e682f02ec46c.png)
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3 . 求下列各式中x的值:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff672ee779dd67bc090caf3053f7225.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ef7c51142e345f62d0db710bcef63f.png)
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解题方法
4 . 已知函数
,当
时,恒有
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0aa2ef928b6e3341d0a0dc6d8055b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1f46f3d31d450248689fdbc7afe202.png)
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5 . 用m,n或b,c表示x,其中m,n,a,b,c均大于0,且
.
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9ba448405a3a304be9c6cfbad27a1c.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5b3e90b617717e7057a3794836c4d0.png)
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6 . 判断下列函数的奇偶性:
(1)
;
(2)
;
(3)
;
(4)
;
(5)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0c844766ffa812c15ac2eb6666c487.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4bfc0f34085652be936540f131a206.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa2b36c56551020b9ebe4576ed409105.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc8382e231e002fd032c922a9c17cbb.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a4ad0af2381a63ceece2d8adff7ace.png)
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7 . 已知下列不等式成立,比较m,n的大小:
(1)
;
(2)
;
(3)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a88d3c5f9b357568485435d9b4ceeb.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba63d88448df1dd95ae8865fd2a7f1d.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f259d42fa56f0b25cd24bf323ea38b09.png)
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解题方法
8 . 比较下列各题中两个数的大小:
(1)
,
;
(2)
,
;
(3)
,
;
(4)
,
(
,
).
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c7d1356f5cbf9d5d4f0a2aff37180a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bef54275f4e9e8ef9ded08e51997fe.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc3838b938a5908f907591190c81d19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c428e57083c670001701f1f77efc870b.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d775e7b8db68662937e88754421bbf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6266400e2f67ea46c0999179febd1ddb.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38adf264cfcf55a806607dc44497571b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e8e9c327ce93fe75e7f049ee157118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
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解题方法
9 . 求下列函数的定义域:
(1)
;
(2)
;
(3)
;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93683f1d2d1cf12b7d5cab32b6a3bbe6.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/660efa11e36c224d7735e831f8b170dc.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e289b4d4d5efe44cbb3f9f384ee494.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13fedfe250205e4b7004fc5d6f08dcae.png)
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10 . 判断下列各式是否恒等(
,且
).
(1)
和
;
(2)
和
;
(3)
和
;
(4)
和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e59d7fda376ea7de5b96e98c9b7c018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd5e7d9dd02334fbf220eee89cdf860.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e168adb7642358ef4c0aa9bcc2efd2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b092abfc01bd3f01bd63f69d79789c.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1938a7a366119f6a33a1d0b8988a591.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ea4b5b10e1f30cb4e9403029259124.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3463d37c72c7a7b0bd4d380361b94de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8a4bd31071ad5884f9d31190d9a3c3.png)
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