對(duì)數(shù)函數(shù)、冪函數(shù)運(yùn)算與圖像性質(zhì)

1、對(duì)數(shù)函數(shù)的運(yùn)算、性質(zhì)以及冪函數(shù)圖像性對(duì)數(shù)函數(shù)的運(yùn)算、性質(zhì)以及冪函數(shù)圖像性質(zhì)一、對(duì)數(shù)函數(shù)的運(yùn)算一、對(duì)數(shù)函數(shù)的運(yùn)算1、對(duì)數(shù)的定義：、對(duì)數(shù)的定義：如果ax=N（a0，a≠1）那么數(shù)x叫做以a為底N的對(duì)數(shù)對(duì)數(shù)。記作:x=logaN，其中ia叫做對(duì)數(shù)的底數(shù)底數(shù)，N叫做真數(shù)真數(shù)，x=logaN叫做對(duì)數(shù)式常用對(duì)數(shù)常用對(duì)數(shù)：log10N=lgN自然對(duì)數(shù)自然對(duì)數(shù)：logeN=lnN2、指數(shù)式和對(duì)數(shù)式的聯(lián)系：、指數(shù)式和對(duì)數(shù)式的聯(lián)系：指數(shù)指數(shù)對(duì)數(shù)對(duì)數(shù)xaN?

2、?(alog0a1)aNx??且3、對(duì)數(shù)的運(yùn)算性質(zhì)、對(duì)數(shù)的運(yùn)算性質(zhì)如果a0，a?1，M0，N0有：；logloglogaaaMNMN??logloglogaaaMMNN??loglog()naaMnMnR??語(yǔ)言表達(dá)語(yǔ)言表達(dá):兩個(gè)正數(shù)的積的對(duì)數(shù)等于這兩個(gè)正數(shù)的對(duì)數(shù)和兩個(gè)正數(shù)的商的對(duì)數(shù)等于這兩個(gè)正數(shù)的對(duì)數(shù)差一個(gè)正數(shù)的n次方的對(duì)數(shù)等于這個(gè)正數(shù)的對(duì)數(shù)n倍給出四個(gè)等式給出四個(gè)等式:1)lg(lg10)02)lg(ln)03)e??2若lgx=1