高中數(shù)學 3.2.1對數(shù)(1)課件 蘇教版必修1.ppt
高中數(shù)學 必修,3.2.1 對數(shù)(1),情境問題:,設x年可實現(xiàn)翻一番的目標,則有,假設2005年我國的國民生產總值為a億元,如每年平均增長8%,那么經過多少年,國民生產總值可翻一番?,a(10.08)x2a,即1.08x2,在指數(shù)式中,已知底數(shù)和指數(shù),通過乘方運算可求冪;而已知指數(shù)和冪,則可通過用開方運算或分數(shù)指數(shù)冪運算求底數(shù);已知底數(shù)和冪,如何求指數(shù)呢?,數(shù)學建構:,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的對數(shù)記作:logaNb,1對數(shù)的定義,a0,a1,bR,N0,abN,對數(shù)式,指數(shù)式,logaNb,底數(shù),指數(shù),冪,底數(shù),真數(shù),對數(shù),數(shù)學應用:,例1將下列各指數(shù)式改寫成對數(shù)式,(1)24=16,(2)33=,(3)5a=20,(4) =0.45,log2164,log3,3,logaabb,log520a,log,0.45b,a,N,logaN,對數(shù)恒等式,對數(shù)是一種運算,對數(shù)是一個結果,對數(shù)的本質,數(shù)學應用:,例2求下列各式的值:,(1)log264,(2)log927,根據(jù)對數(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)學建構:,2關于對數(shù)的幾個要點,(1)負數(shù)和0沒有對數(shù);,(2)常用對數(shù):底數(shù)為10的對數(shù)稱為常用對數(shù),記為lgN;,(3) 自然對數(shù):底數(shù)為e的對數(shù)稱為常用對數(shù),記為lnN,(4)對數(shù)恒等式,數(shù)學應用:,例3將下列對數(shù)式改寫成指數(shù)式,(1) log51253,(3) lga1.699,(2),數(shù)學應用:,例4已知loga2m,loga3n,求a2mn的值,數(shù)學應用:,練習,0,0,0,13,1(1)lg(lg10) ;,(2)lg(lne) ;,(3)log6log4(log381) ;,(4)log3( )1,則x_,數(shù)學應用:,練習,2把logx z表示成指數(shù)式是 ,3設,,則滿足,的x值為_,5設xlog23,求,小結:,abN logaNb,注: (1)負數(shù)和0沒有對數(shù); (2)常用對數(shù)與自然對數(shù); (3)對數(shù)恒等式,作業(yè):,P79習題3.2(1)1,2,3(1)(4),