對(duì)數(shù)函數(shù)換底公式(課堂PPT)

1、1積、商、冪的對(duì)數(shù)運(yùn)算法則：積、商、冪的對(duì)數(shù)運(yùn)算法則：如果如果a0，且，且a1，M0，N0有：有：NMMNaaaloglog)(logNMNMaaalogloglogR)M(nnManaloglogMnPMManPanpalogloglog)(logRnnananaaaaMMMMMlogloglog)M(log21n21MMaalog1log2一、對(duì)數(shù)的換底公式一、對(duì)數(shù)的換底公式: 如何證明呢如何證明呢?aNNccalogloglog)0), 1()1 , 0(,( Nca3證明證明：設(shè)：設(shè) 由對(duì)數(shù)的定義可以得：由對(duì)數(shù)的定義可以得： paN 即證得即證得 pNalogpccaNloglogap

2、NccloglogaNpccloglogaNNccalogloglog通過(guò)換底公式，人們通過(guò)換底公式，人們可以把其他底的對(duì)數(shù)可以把其他底的對(duì)數(shù)轉(zhuǎn)換為以轉(zhuǎn)換為以10或或e為底為底的對(duì)數(shù)，經(jīng)過(guò)查表就的對(duì)數(shù)，經(jīng)過(guò)查表就能求出任意不為能求出任意不為1的的正數(shù)為底的對(duì)數(shù)。正數(shù)為底的對(duì)數(shù)。4二、幾個(gè)重要的推論二、幾個(gè)重要的推論: 如何證明呢如何證明呢?abbalog1logNmnNanamloglog), 1 () 1 , 0(,ba5證明證明：利用換底公式得：利用換底公式得：即證得即證得 NmnNanamlogloglglglgloglglglgmnaNnNnNnNamamamlogaNmnaNlglg

3、6證明證明:由換底公式由換底公式 abbalog1log即即 abbaloglog1lglglglgbaab1logloglogacbcba推論推論:7例例1:計(jì)算計(jì)算:解解: 27log19 27log19333log23log23323 8log7log3log2732 9lg212log11003338 9lg212log1100333 8log7log3log27322lg2lg32lg3lg3lg7lg7lg8lg3解解:例例1:計(jì)算計(jì)算: 27log19 8log7log3log27329解解: 9lg212log11003339lg2122log103339lg102392315

4、 9lg212log1100333例例1:計(jì)算計(jì)算: 27log19 8log7log3log273210解解:.)21(2,10054:2的值求設(shè)例baba10054ba10log10log100log22242a2log224log245log100log55255b2log1110log12)21(252ba25log2log22log5log12log21010551011. 9log,7log,5log:33539表示試用已知例nmnm解解:7log, 5log215log5log33392nm7log,25log33nmnm227log5log235log23log29log333353512.,07lg5lglg)7lg5(lglg:421212xxxxxx求的兩根分別為方程例07lg5lglg)7lg5(l