名校
1 . 已知函数
.
(1)若
,求方程
的解集;
(2)若函数
的最小值为
,求实数a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10dda958e0a26731d73c3127f9ad484.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f9a575fc639253a8efe28ab73a985e.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a711a0b8c90ec23b7d449c0709746cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e35f76e01c3979ae5987f7729f9856.png)
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解题方法
2 . 求解下列问题:
(1)已知
,
,求
的值.
(2)求
的值.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d7acaa3fe60e42621516fce4d12768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413e508a980a278ad1480fea1111a718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cebe06d0c9ffa4bdd7ed79dfbe1b19fe.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae41b71f234d337a57e52d67ee7ca15b.png)
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3 . 化简求值:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72521916f1cb5e9a0d1cddf6f5154877.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72521916f1cb5e9a0d1cddf6f5154877.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe92233c8df7580e35c5df4cc104dfe.png)
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4 . 经验表明,某种日照绿茶用80℃的水泡制,再等到茶水温度降至60℃时,饮用口感最佳.为方便控制水温,某研究小组采用了物体在常温环境下温度变化的冷却模型;若物体的初始温度是
℃,室温是
℃,则经过时间
(单位;分钟)后物体的温度
(单位:℃)满足
,其中
为正常数.研究小组通过多次测量取平均值的方法,测得200mL初始温度为85℃的茶水,放在室温25℃的环境中自然冷却,10分钟以后茶水的温度降至55℃.
(1)求
的值;
(2)当室温为20℃时,若该种日照绿茶用80℃的水泡制,自然冷却至60℃,可以产生最佳口感,那么,则刚泡好的茶水大约需要放置多长时间才能达到最佳饮用口感?(结果精确到0.1)(附,参考值
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6861ea66b004cf4b9058032e2d3df15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)当室温为20℃时,若该种日照绿茶用80℃的水泡制,自然冷却至60℃,可以产生最佳口感,那么,则刚泡好的茶水大约需要放置多长时间才能达到最佳饮用口感?(结果精确到0.1)(附,参考值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/400f57f3bc59cf9032aeba473b8553b1.png)
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名校
5 . (1)计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a35d6c9bd23a6ff097c27391cf51f4c.png)
(2)求下列式中的
的值:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a35d6c9bd23a6ff097c27391cf51f4c.png)
(2)求下列式中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5e0c6462e32865cc17c0364457fc4d.png)
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2023-12-20更新
|
954次组卷
|
3卷引用:山东省枣庄市市中区辅仁高级中学2023-2024学年高一上学期11月月考数学试题
山东省枣庄市市中区辅仁高级中学2023-2024学年高一上学期11月月考数学试题吉林省长春市第八中学2023-2024学年高一上学期期中数学试题(已下线)【第二练】4.3.1对数的概念+4.3.2对数的运算【第二练】上好三课,做好三套题,高中数学素养晋级之路
名校
6 . 化简求值:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feef7f8c28ae8a2c9a67d7fea22944c2.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feef7f8c28ae8a2c9a67d7fea22944c2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce88b05d5f5b67125dd45a231bd856fb.png)
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7 . (1)求值:
.
(2)已知正数
满足
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77119654b4259e8f15a27d40ad42e37b.png)
(2)已知正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a655028a614c26f1eb4700422fd9a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7467b638d3a7418d8301f415daca18c7.png)
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2023-11-30更新
|
606次组卷
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5卷引用:山东省临沂第十八中学2023-2024学年高一上学期第三次月考考前模拟数学试题
8 . 已知数列
,满足
且点
在函数
的图像上,且
.
(1)证明:
是等比数列.并求
.
(2)令
,设
的前
项和
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a189f5f230b75af75eed2a5ff0f24b1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69b76612264b62b3e66947e71707ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88aef647186022d30b0e719126d6465.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d8f2f15adae9848373de1ab8c7bc7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74e9c7610cbf2bda17bd7206969fb599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105de1b20942840a12712c6795a05e1b.png)
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名校
9 . 化简求值:
(1)
;
(2)若
,求
的值.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26460251178da65240510f996b3f1755.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d873727b837fd3acdce4aa0fcdfbe54d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db09a66515a0caa4291d1078fc7661a.png)
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2023-11-19更新
|
661次组卷
|
2卷引用:山东省泰安市新泰第一中学老校区(新泰中学)2023-2024学年高一上学期期中考试数学试题
10 . (1)计算
的值;.
(2)
;
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84ce70743afafb9b79594c1f7bf145b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e359574da3221002403d0150b1e93c.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0eb4ecc9302534d98a42a80aa9f73d7.png)
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