1、高中數(shù)學(xué) 必修,3.2.1對(duì)數(shù)（1）,情境問題：,設(shè)x年可實(shí)現(xiàn)翻一番的目標(biāo)，則有,假設(shè)2005年我國(guó)的國(guó)民生產(chǎn)總值為a億元，如每年平均增長(zhǎng)8%，那么經(jīng)過多少年，國(guó)民生產(chǎn)總值可翻一番？,a(10.08)x2a，即1.08x2,在指數(shù)式中，已知底數(shù)和指數(shù)，通過乘方運(yùn)算可求冪；而已知指數(shù)和冪，則可通過用開方運(yùn)算或分?jǐn)?shù)指數(shù)冪運(yùn)算求底數(shù)；已知底數(shù)和冪，如何求指數(shù)呢？,數(shù)學(xué)建構(gòu)：,一般地，如果a (a0，a1 )的b次冪等于N，即abN那么就稱b為以a為底的N的對(duì)數(shù)記作：logaNb,1對(duì)數(shù)的定義,a0，a1,bR,N0,abN,對(duì)數(shù)式,指數(shù)式,logaNb,底數(shù),指數(shù),冪,底數(shù),真數(shù),對(duì)數(shù),數(shù)學(xué)應(yīng)用：,

2、例1將下列各指數(shù)式改寫成對(duì)數(shù)式,(1)24=16,(2)33=,(3)5a=20,(4) =0.45,log2164,log3,3,logaabb,log520a,log,0.45b,a,N,logaN,對(duì)數(shù)恒等式,對(duì)數(shù)是一種運(yùn)算,對(duì)數(shù)是一個(gè)結(jié)果,對(duì)數(shù)的本質(zhì),數(shù)學(xué)應(yīng)用：,例2求下列各式的值:,(1)log264,(2)log927,根據(jù)對(duì)數(shù)的定義，寫出下列各式的值(其中a0，a1 ),(1)log10100,(2)log255,(3)log2,(4)log,(5)log33,(6)logaa,(7)log31,(8)loga1,3,2,1,1,1,1,0,0,數(shù)學(xué)建構(gòu)：,2關(guān)于對(duì)數(shù)的幾個(gè)要點(diǎn),

3、(1)負(fù)數(shù)和0沒有對(duì)數(shù)；,(2)常用對(duì)數(shù)：底數(shù)為10的對(duì)數(shù)稱為常用對(duì)數(shù)，記為lgN；,(3) 自然對(duì)數(shù)：底數(shù)為e的對(duì)數(shù)稱為常用對(duì)數(shù)，記為lnN,(4)對(duì)數(shù)恒等式,數(shù)學(xué)應(yīng)用：,例3將下列對(duì)數(shù)式改寫成指數(shù)式,(1) log51253,(3) lga1.699,(2),數(shù)學(xué)應(yīng)用：,例4已知loga2m，loga3n，求a2mn的值,數(shù)學(xué)應(yīng)用：,練習(xí),0,0,0,13,1(1)lg(lg10) ；,(2)lg(lne) ；,(3)log6log4(log381) ；,(4)log3( )1，則x_,數(shù)學(xué)應(yīng)用：,練習(xí),2把logx z表示成指數(shù)式是 ,3設(shè),，則滿足,的x值為_,5設(shè)xlog23，求,小結(jié)：,abN logaNb,注： (1)負(fù)數(shù)和0沒有對(duì)數(shù)； (