2022年人教A版数学必修一2.2.1《对数与对数运算》学案2 .pdf

名师精编优秀教案重庆市万州分水中学高中数学 2.2.1 对数与对数运算（2）学案 新人教 A版必修 1 学习目标1.掌握对数的运算性质，并能理解推导这些法则的依据和过程；2.能较熟练地运用对数运算法则解决问题.学习过程一、课前准备（预习教材P64 P66，找出疑惑之处）复习 1：（1）对数定义：如果xaN(0,1)aa，那么数x叫做，记作 .（2）指数式与对数式的互化：xaN .复习 2：幂的运算性质.（1）mnaa；（2）()mna；（3）()nab .复习 3：根据对数的定义及对数与指数的关系解答：（1）设log 2am，log 3an，求m na；（2）设logaMm，logaNn，试利用 m、n 表 示log(aM)N二、新课导学 学习探究探究任务：对数运算性质及推导问题：由pqp qa aa，如何探讨logaMN和logaM、logaN之间的关系？问题：设logaMp,logaNq，由对数的定义可得：M=pa，N=qaMN=paqa=p qa，logaMN=p+q，即得logaMN=logaM+logaN根据上面的证明，能否得出以下式子？如果a 0，a 1，M 0，N 0，则（1）log()loglogaaaMNMN；（2）logloglogaaaMMNN；（3）loglog()naaMnMnR.名师精编优秀教案反思：自然语言如何叙述三条性质？性质的证明思路？（运用转化思想，先通过假设，将对数式化成指数式，并利用幂运算性质进行恒等变形；然后再根据对数定义将指数式化成对数式）典型例题例 1 用logax,logay,logaz表示下列各式：（1）2logaxyz；（2）35logaxyz.例 2 计算：（1）5log 25；（2）0.4log1；（3）852log(42)；（4）lg9100.探究：根据对数的定义推导换底公式logloglogcacbba（0a，且1a；0c，且1c；0b）文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9名师精编优秀教案试试：2000 年人口数13 亿，年平均增长率1，多少年后可以达到18 亿？动手试试练 1.设lg 2a,lg3b，试用a、b表示5log 12.变式：已知lg2 0.3010，lg3 0.4771，求 lg6、lg12.lg3的值.练 2.运用换底公式推导下列结论.（1）loglogmnaanbbm；（2）1loglogabba.练 3.计算：（1）7lg142lglg 7lg183；（2）lg 243lg9.三、总结提升 学习小结对数运算性质及推导；运用对数运算性质；换底公式.文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 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HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9名师精编优秀教案 知识拓展 对数的换底公式logloglogbabNNa；对数的倒数公式1loglogabba.对数恒等式：loglognnaaNN，loglogmnaanNNm，logloglog1abcbca.学习评价 自我评价你完成本节导学案的情况为（）.A.很好 B.较好 C.一般 D.较差 当堂检测（时量：5 分钟满分：10 分）计分：1.下列等式成立的是（）A222log(35)log 3log 5B222log(10)2log(10)C222log(35)log 3log 5D3322log(5)log 52.如果lgx=lga+3lgb 5lgc，那么（）.Ax=a+3bc B35abxcC35abxcD x=a+b3c33.若 2lg2lglgyxxy，那么（）.A yx B 2yxC3yx D 4yx4.计算：（1）99log 3log 27；（2）2121loglog22 .5.计算：315lglg523 .课后作业1.计算：（1）lg27lg83lg10lg1.2；（2）2lg 2lg 2 lg5lg5.2.设 a、b、c 为正数，且346abc，求证：文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 HF3N5Q2P10E1 ZE1K10P6X2Y9文档编码:CZ5G4C5G7T7 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