1 . 设
,
,
,且
,
,利用对数的换底公式证明:
(1)
;
(2)
.
![](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/ea4313f830e9be762a14205f2c2141d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406185f4ad8bcd99e23adc8d289088ed.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4eebfbd681b6faa2f721ce6255e0be7.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e17444a36dc88474cedf3d1c1a2288a.png)
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2023-10-08更新
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269次组卷
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8卷引用:2.2 换底公式
(已下线)2.2 换底公式北师大版(2019)必修第一册课本习题第四章2.2换底公式(已下线)4.3 对数(6大题型)精讲-【题型分类归纳】(人教A版2019必修第一册)(已下线)2.2换底公式-同步精品课堂(北师大版2019必修第一册)(已下线)【第三课】4.3.1对数的概念+4.3.2对数的运算【第三课】上好三课,做好三套题,高中数学素养晋级之路(已下线)4.3对数北师大版(2019)必修第一册课本例题2.2 换底公式【导学案】2.2 换底公式课前预习-北师大版2019必修第一册第四章对数运算与对数函数
2 . 求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3594c29c92c03a94e6e22479892af3.png)
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2023-10-08更新
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195次组卷
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4卷引用:2.2 换底公式
(已下线)2.2 换底公式北师大版(2019)必修第一册课本习题第四章2.2换底公式(已下线)4.3 对数(6大题型)精练-【题型分类归纳】(人教A版2019必修第一册)北师大版(2019)必修第一册课本例题2.2 换底公式
3 . 已知
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b35fa8653fe660bdd23bb473b8f904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8548de3171db215c876e46c42f6878.png)
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23-24高二上·上海·课后作业
4 . 已知
是等比数列,当
时,其中
、
、
、
均为正整数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6fb1dbeaaa23449ccfec570b9433ec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5bd839754cc26795de089abcbb0820c.png)
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23-24高二上·上海·课后作业
解题方法
5 . (1)已知
,
,
成等差数列,其公差为
.求证:
,
,
成等比数列.
(2)已知正实数
,
,
成等比数列,其公比为
.求证:
,
,
成等差数列.
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ef024c58becb626b823dfd3ee99c1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec9a109b4ff41dc4d7716fa776f450f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92f2d6b743b57500fb4ba695ec160f27.png)
(2)已知正实数
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24106d94bf13cac0501cdb695b9972c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489ac3f68848980d53033dbd65a0a622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba73c0fc1d96654151175cc84b792c7.png)
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6 . 已知
.
(1)求
的定义域和值域;
(2)判断并证明
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd54ec804218ea006591d26241b1f667.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断并证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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7 . 已知函数
.
(1)求证:
是奇函数;
(2)用单调性的定义证明:
在R上是增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362bfce584209628bc4ad3f23e3d7b11.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用单调性的定义证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2023-08-28更新
|
439次组卷
|
3卷引用:人教A版(2019) 必修第一册 数学奇书 第四章 指数函数与对数函数 4.2 指数函数 第2课时 指数函数的图象和性质的应用
人教A版(2019) 必修第一册 数学奇书 第四章 指数函数与对数函数 4.2 指数函数 第2课时 指数函数的图象和性质的应用新疆喀什地区泽普县第二中学2024届高三上学期第一次月考数学试题(已下线)6.2 指数函数(2)-【帮课堂】(苏教版2019必修第一册)
解题方法
8 . 函数
对任意的实数
,
有
,当
时,有
.
(1)求证:
;
(2)若
在
上为严格增函数,且
,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77059d2f66926c6a5b535ccef6aa1490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104375baf5cef5eb92cfc7cf13b80193.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a19bbab2270fc8e694527e801556cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3439cfe3a2af9a571bf9033cd6959cb9.png)
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名校
9 . 已知
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a3a74aa69599f96e568c15602293b16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a16e990f8be8af5202244976e5e5bd.png)
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名校
解题方法
10 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375cf32b61c309085bc7eb562d213e70.png)
(1)判断
在区间
上的单调性,并用定义证明;
(2)记函数
,问:是否存在实数
使得函数
为偶函数?若存在,请求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344d591ddf40ec7c27aa95c54eea961f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375cf32b61c309085bc7eb562d213e70.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
(2)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327f44ff2ac549a0930f0948be0e9468.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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