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1 .
计算:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a928686a08e36ecad476ed0eabfbc523.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03bfe30380decb4ba3f9a6b0598ed922.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a928686a08e36ecad476ed0eabfbc523.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e4a51e1a8cb1c68b6dfe16bef53766.png)
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2 . 计算
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8dc897339f46208a45ed0f051c2a15b.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8dc897339f46208a45ed0f051c2a15b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3c4e9daaee2a6a13aa5d421c3c3361.png)
您最近一年使用:0次
2023-09-19更新
|
618次组卷
|
4卷引用:宁夏银川市永宁县三沙源上游高级中学2023-2024学年高一上学期第三次月考数学试题
宁夏银川市永宁县三沙源上游高级中学2023-2024学年高一上学期第三次月考数学试题湖南省岳阳市平江县颐华高级中学(平江)有限公司2022-2023学年高一下学期开学考试数学试题(已下线)4.3 对数(AB分层训练)-【冲刺满分】(已下线)专题4.8 指数函数与对数函数全章综合测试卷(基础篇)-举一反三系列
3 . 数学运算是指在明晰运算对象的基础上,依据运算法则解决数学问题的素养.对数运算与指数幂运算是两类重要的运算.
例如:设
,
,则
,
.又因为
,所以
.即![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb70b167082e01f9d7b24bf5efd8cb25.png)
(1)同样地,同学们可以由
根据所学知识推导如下的对数运算性质,或者发散自己的思维尝试利用其它的方法推导如下的运算性质:如果
,且
,
,那么
;
(2)请你运用(1)中的对数运算性质计算
的值.
例如:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/043a0ba27f3978ec44153dde255eaa95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68add55801760523293d53275eea2512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee735f5408eb434ee41ec2b79bb0aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56505c820a05e7ba5cc156b7d7cc3fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181c4f1e03860b61a390891bbcec9d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b0381421e7f5c2c6618b3e859a3961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb70b167082e01f9d7b24bf5efd8cb25.png)
(1)同样地,同学们可以由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2444f9b118a5f3b0dcf7dd9a70e9efc1.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/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da14e82f6e67364330dd788d5c43feb.png)
(2)请你运用(1)中的对数运算性质计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d04fb0e77ae84eac3778e2515e07ff0.png)
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解题方法
4 . 已知
(
且
).
(1)证明:函数
是偶函数;
(2)当
时,若函数
只有一个零点,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3536fe8307878a8c880b616f7e8021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a614be032089ad72971370afe0f04089.png)
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2023-02-19更新
|
446次组卷
|
2卷引用:宁夏银川市唐徕中学2022-2023学年高一上学期期末考试数学试题
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5 . 计算化简
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88baa570dfdf1b18056c3c9816fe1d4.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88baa570dfdf1b18056c3c9816fe1d4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736b27a97832ad20b1204ea6396f03cb.png)
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解题方法
6 . 习近平总书记在十九大报告中指出,“要着力解决突出环境问题,持续实施大气污染防治行动".为落实好这一精神,市环保局规定某工厂产生的废气必须过滤后才能排放.已知在过滤过程中,废气中的污染物含量
(单位:毫克/升)与过滤时间
(单位:小时)之间的函数关系式为
(
为自然对数的底数,
为污染物的初始含量).过滤1小时后检测,发现污染物的含量为原来的
.
(1)求函数
的关系式;
(2)要使污染物的含量不超过初始值的
,至少需过滤几小时?(参考:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd0ee199569564ead4840cb3fddfdeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8f69402300f6ed932697689212e91c.png)
(2)要使污染物的含量不超过初始值的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38c5688914317f4a6eef630cba36d08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8f5b560c5cea567a5e5c3462085b43.png)
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2022-12-08更新
|
664次组卷
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3卷引用:宁夏银川市贺兰县景博中学2022-2023学年高一上学期第二次月考数学试题
7 . (1)计算:
;
(2)计算:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f1f1f2c0ea447de6c663b18e87e50.png)
(2)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6dd826cba7a0123c2988f3ea5b6ff7.png)
您最近一年使用:0次
2022-12-07更新
|
246次组卷
|
2卷引用:宁夏银川市贺兰县景博中学2022-2023学年高一上学期第二次月考数学试题
8 . 计算化简:
(1)
;
(2)
;
(3)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810c1fdcce5af60b9e94c6b97c48f607.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052bd20be4a9b806244cf3fe739ea1b0.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d991a2ebd848da250882c9c776eb039d.png)
您最近一年使用:0次
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9 . 计算.
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2570e883284e909b3c60d36e9dd705.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774226060822e099d013f2033af1602f.png)
您最近一年使用:0次
2022-11-21更新
|
426次组卷
|
2卷引用:宁夏银川市第二中学2022-2023学年高一上学期期中考试数学试题
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10 . 计算:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce96b3a103c95bd19a270d8033020d3.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434dae23b4081314a022340b4d91c877.png)
您最近一年使用:0次
2022-11-21更新
|
1636次组卷
|
6卷引用:宁夏回族自治区银川一中2022-2023学年高一上学期期中考试数学试题