[考綱傳真] 1.理解對(duì)數(shù)的概念及其運(yùn)算性質(zhì),知道用換底公式將一般對(duì)數(shù)轉(zhuǎn)化成自然對(duì)數(shù)或常用對(duì)數(shù);了解對(duì)數(shù)在簡(jiǎn)化運(yùn)算中的作用.2.理解對(duì)數(shù)函數(shù)的概念及其單調(diào)性,掌握對(duì)數(shù)函數(shù)圖像通過(guò)的特殊點(diǎn),會(huì)畫底數(shù)為2,10,的對(duì)數(shù)函數(shù)的圖像.3.體會(huì)對(duì)數(shù)函數(shù)是一類重要的函數(shù)模型.4.了解指數(shù)函數(shù)y=ax(a>0,且a≠1)與對(duì)數(shù)函數(shù)y=logax(a>0,且a≠1)互為反函數(shù).
1.對(duì)數(shù)的概念
如果a(a>0,a≠1)的b次冪等于N,即ab=N,那么數(shù)b叫作以a為底N的對(duì)數(shù),記作logaN=b,其中a叫作對(duì)數(shù)的底數(shù),N叫作真數(shù).
2.對(duì)數(shù)的性質(zhì)與運(yùn)算法則
(1)對(duì)數(shù)的運(yùn)算法則:如果a>0,且a≠1,M>0,N>0,那么:
①loga(M·N)=logaM+logaN;
②loga=logaM-logaN;
③logaMn=nlogaM(n∈R).
(2)對(duì)數(shù)的性質(zhì):①alogaN=N;②logaab=b(a>0,且a≠1).
(3)對(duì)數(shù)的換底公式:logab=(a,c均大于0