對(duì)數(shù)對(duì)數(shù)已知指數(shù)已知指數(shù)b,冪冪N,求底數(shù)求底數(shù)a 開(kāi)方運(yùn)算開(kāi)方運(yùn)算 ,根式根式,其中其中a:方根方根,b:根指數(shù)根指數(shù),N:被開(kāi)方被開(kāi)方數(shù)數(shù)其中其中a0且且a1,bR,N0已知底數(shù)已知底數(shù)a,指數(shù)指數(shù)b,求冪求冪N 乘方運(yùn)算乘方運(yùn)算 N=ab , 指數(shù)式指數(shù)式 , 其中其中 a:底數(shù)底數(shù),b:指數(shù)指數(shù),N:冪冪已知底數(shù)已知底數(shù)a,冪冪N,求指數(shù)求指數(shù)b 對(duì)數(shù)運(yùn)算對(duì)數(shù)運(yùn)算 b=logaN ,對(duì)數(shù)式對(duì)數(shù)式, 其中其中a:底數(shù)底數(shù),b:對(duì)數(shù)對(duì)數(shù),N:真數(shù)真數(shù) 實(shí)數(shù)指數(shù)冪實(shí)數(shù)指數(shù)冪ab=NbNa 一般地一般地,如果如果a(a0,a1)的的b次冪等于次冪等于N,就是就是ab=N,那么數(shù)那么數(shù)b叫做叫做以以a為底的為底的N對(duì)數(shù)對(duì)數(shù),記記作作logaN=b,其中其中a叫做叫做對(duì)數(shù)的底數(shù)對(duì)數(shù)的底數(shù),N叫做叫做真真數(shù)數(shù). a b = N log a N = b冪冪 N0 真數(shù)真數(shù)底數(shù)底數(shù)a0,且且a1底數(shù)底數(shù)指數(shù)對(duì)數(shù)因此，要使對(duì)數(shù)因此，要使對(duì)數(shù)loga有意義必須有有意義必須有底數(shù)底數(shù)a0并且并且a1和和真數(shù)真數(shù) 幾個(gè)重要結(jié)論幾個(gè)重要結(jié)論(其中其中a0且且a0,N0) 零和負(fù)數(shù)沒(méi)有對(duì)數(shù)零和負(fù)數(shù)沒(méi)有對(duì)數(shù) logaa=1 3 loga1=0 4 alogaN=NWhy? 特殊常用的兩種對(duì)數(shù)特殊常用的兩種對(duì)數(shù)（）常用對(duì)數(shù)（）常用對(duì)數(shù) 以以10為底的對(duì)數(shù)叫做常用對(duì)數(shù)，即對(duì)數(shù)為底的對(duì)數(shù)叫做常用對(duì)數(shù)，即對(duì)數(shù)logaN(a0且且a1)(）在底數(shù)）在底數(shù)a=10時(shí)，叫做常用對(duì)數(shù)，的常用對(duì)數(shù)時(shí)，叫做常用對(duì)數(shù)，的常用對(duì)數(shù)log10N簡(jiǎn)記作簡(jiǎn)記作lgN例如例如log105=lg5 ( 2 ) 自然對(duì)數(shù)自然對(duì)數(shù) 以無(wú)理數(shù)以無(wú)理數(shù)e2.71828為底的對(duì)數(shù)叫做自然對(duì)數(shù)，即對(duì)數(shù)為底的對(duì)數(shù)叫做自然對(duì)數(shù)，即對(duì)數(shù)logaN(a0且且a1)(）在底數(shù)）在底數(shù)a=e時(shí)，叫做自然對(duì)數(shù)，的自時(shí)，叫做自然對(duì)數(shù)，的自然對(duì)數(shù)然對(duì)數(shù)logeN簡(jiǎn)記作簡(jiǎn)記作lnN例如例如 loge5=ln5lg10=1, lg1=0lne=1, ln1=0例1.將下列指數(shù)式寫(xiě)成對(duì)數(shù)式mexxma )6(710)5(73. 5)31)(4(273)3(6412)2(6255) 1 (64 例2.將下列對(duì)數(shù)式寫(xiě)成指數(shù)式303.210ln)4(201.0lg)3(7128log)2(416log)1(221 對(duì)數(shù)的運(yùn)算性質(zhì)對(duì)數(shù)的運(yùn)算性質(zhì)NMMNaaaloglog)(log)( 1 1NMaaNMalogloglog)( 2 2MnManaloglog)3(RnNMaa , 0, 0, 1, 0 且且其其中中，abbccalogloglog)4( bbamnnamloglog)5( 1loglog)6( abba例例3 用用logax,logay,logaz表示下列各式表示下列各式32log)2(log)1(zyxzxyaa例4 求下列各式的值5572100lg)2()24(log)1(