第4章 指数与对数
能力过关卷
一、单项选择题:(本题共8小题,每小题5分,共40分.在每小题给出的四个选项中,只有一项是符合题目要求的.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0003ced2620460824334f14c6fbdfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c4567a1c1c7d73a2d0179881f497ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a8ec10095b9053bfe661fe620fe86e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
【知识点】 对数的运算 运用换底公式化简计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44210e158fad9be7cb088966f2b01c07.png)
A.2 | B.![]() |
C.4 | D.![]() |
【知识点】 对数的运算性质的应用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b51558f103a7d4154e47814521de67.png)
A.1 | B.2 | C.3 | D.4 |
【知识点】 对数的运算 运用换底公式化简计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da63609b218a9bad8842ea15a158438e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ed18619e71aa3e0515919a3cd96959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f477a82ef73df97887be47c931cedd.png)
A.充分不必要条件 | B.必要不充分条件 | C.充要条件 | D.既不充分也不必要条件 |
【知识点】 判断命题的充分不必要条件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de380e22fe3741440d95835053eb094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fc838e1477179b36ca7481ee2cc1e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
A.5 | B.3 | C.2 | D.1 |
【知识点】 对数的运算性质的应用 基本不等式“1”的妙用求最值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49935d350ff851af0514e4889d353ce9.png)
A.1010.1 | B.10.1 | C.lg10.1 | D.![]() |
【知识点】 对数的运算
二、多项选择题:(本题共4小题,每小题5分,共20分.在每小题给出的选项中,有多项符合题目要求.全部选对的得5分,有选错的得0分,部分选对的得3分.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408c639795222936f9c30b11117a9756.png)
A.![]() | B.![]() | C.![]() | D.![]() |
【知识点】 指数式与对数式的互化 对数的运算 对数的运算性质的应用
A.(![]() ![]() | B.![]() ![]() | C.![]() ![]() | D.![]() ![]() |
【知识点】 分数指数幂与根式的互化
A.a+b=2 | B.b﹣a=1 | C.ab>8lg22 | D.b﹣a<lg6 |
【知识点】 指数式与对数式的互化 对数的运算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85cd387ef073772decae903f476f4e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efdc0e0ca559f0f1af6127545f356fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1817297374e431a1d9087dcc2991d3a9.png)
A.![]() | B.![]() | C.![]() | D.2 |
【知识点】 对数的运算 对数的运算性质的应用
三、填空题:(本题共4小题,每小题5分,共20分.)
![](https://img.xkw.com/dksih/QBM/2020/7/25/2513075641016320/2513729521934336/STEM/10e0bd3de1084f739a5b8fd5bc32bb50.png?resizew=93)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303f67f6d5a3f50d5a54839815c4a1fd.png)
【知识点】 指数幂的运算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d66cfc300dde99af91b689021b62974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
【知识点】 指数式与对数式的互化
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d83c3f5989deb2db93829173692c8e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af88528e1a22bc93e140b6c734659689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e4bc422b72dd83ac292b35c010d9fa.png)
【知识点】 对数的运算
四、解答题:(本题共6小题,共70分.解答应写出文字说明、证明过程或演算步骤.)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e320dfc8c25b36392d1737c5d7f69f1.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e123a077810d36b43de3569a50614d2c.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e93050e2a98462db9996834d7c17a67.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041782a7c1dc7e06cc9644008d306725.png)
【知识点】 对数的运算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6160731a591932b7b1e29c82ab111a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
【知识点】 指数式与对数式的互化
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f1a77df4f43746a2e3fa334503ae0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af43a57ddd3339250971a6cf603a733b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ecd243f470dfad138cfb1fb9b6347f.png)
【知识点】 指数式与对数式的互化 对数的运算