342換底公式課件（北師大版必修一）

1、欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)42換底公式換底公式欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)學(xué)習(xí)導(dǎo)航學(xué)習(xí)導(dǎo)航學(xué)習(xí)目標(biāo)學(xué)習(xí)目標(biāo)欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)重點(diǎn)難點(diǎn)重點(diǎn)難點(diǎn)重點(diǎn)：換底公式的特征重點(diǎn)：換底公式的特征難點(diǎn)：用換底公式進(jìn)行對(duì)數(shù)式的化簡(jiǎn)求值難點(diǎn)：用換底公式進(jìn)行對(duì)數(shù)式的化簡(jiǎn)求值欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)知識(shí)回顧：知識(shí)回顧：1對(duì)數(shù)的基本性質(zhì)對(duì)數(shù)的基本性質(zhì)(1)零和負(fù)數(shù)零和負(fù)數(shù)_對(duì)數(shù)；對(duì)數(shù)；(2) _ (a0，a1)；(3)loga1_ (a0，a1)；(4)loga

2、a_ (a0，a1)沒(méi)有沒(méi)有N01logaaN?底數(shù)?對(duì)數(shù)?真數(shù)?冪?指數(shù)?底數(shù)?log?a?Nb?a?b?=N(a0a1,N0)且欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)2對(duì)數(shù)的運(yùn)算性質(zhì)對(duì)數(shù)的運(yùn)算性質(zhì)如果如果a0，a1，M0，N0，則：，則：(1)loga(MN)_；(2)logaMn_ (nR)；logaMlogaNnlogaMlogaMlogaN欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)新知初探新知初探思維啟動(dòng)思維啟動(dòng)對(duì)數(shù)換底公式對(duì)數(shù)換底公式logbN_(a，b0，a，b1，N0).注：換底公式常換成自然對(duì)數(shù)或常用對(duì)數(shù)。注：換底公式常換成自然

3、對(duì)數(shù)或常用對(duì)數(shù)。想一想想一想1.證明換底公式？證明換底公式？2.logab與與logba(a0，a1，b0，b1)有什有什么關(guān)系？么關(guān)系？欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)做一做做一做 欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)2log47log74等于等于()A0 B1C4 D7欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)想一想想一想2.(logab)(logbc)(logca)(a，b，c0且且a，b，c1)的值是多少？的值是多少？欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)題型一題型一用換底公式求

4、對(duì)數(shù)式的值用換底公式求對(duì)數(shù)式的值 計(jì)算：計(jì)算：(1)log1627log8132；(2)(log32log92)(log43log83) 欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)【思維總結(jié)】【思維總結(jié)】求對(duì)數(shù)式的值時(shí)，若底數(shù)不求對(duì)數(shù)式的值時(shí)，若底數(shù)不同，可用換底公式化為同底，再利用對(duì)數(shù)運(yùn)同，可用換底公式化為同底，再利用對(duì)數(shù)運(yùn)算性質(zhì)計(jì)算算性質(zhì)計(jì)算欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù) 思：用換底公式證明思：用換底公式證明 logab(a，b0，a，b1)namblogmn欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)變式訓(xùn)練變式

5、訓(xùn)練1計(jì)算計(jì)算(log2125log425log85)(log52log254log1258)欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)題型二題型二用已知對(duì)數(shù)表示其它對(duì)數(shù)用已知對(duì)數(shù)表示其它對(duì)數(shù) 已知已知log189a,18b5，試用，試用a，b表示表示log3645. 欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)【名師點(diǎn)睛】【名師點(diǎn)睛】求條件對(duì)數(shù)式的值，可從條求條件對(duì)數(shù)式的值，可從條件入手，從條件中分化出要求的對(duì)數(shù)式，進(jìn)件入手

6、，從條件中分化出要求的對(duì)數(shù)式，進(jìn)行求值；也可從結(jié)論入手，轉(zhuǎn)化成能使用條行求值；也可從結(jié)論入手，轉(zhuǎn)化成能使用條件的形式；還可同時(shí)化簡(jiǎn)條件和結(jié)論，直到件的形式；還可同時(shí)化簡(jiǎn)條件和結(jié)論，直到找到它們之間的聯(lián)系找到它們之間的聯(lián)系欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)變式訓(xùn)練變式訓(xùn)練欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)題型三利用對(duì)數(shù)求值題型三利用對(duì)數(shù)求值【思路點(diǎn)撥】【思路點(diǎn)撥】把把a(bǔ)，b用對(duì)數(shù)形式表示后，用對(duì)數(shù)形式表示后，轉(zhuǎn)化為對(duì)數(shù)的運(yùn)算求值轉(zhuǎn)化為對(duì)數(shù)的運(yùn)算求值【解】：由【解】：由3a4b36，得，得log336a，log436b，欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)變式訓(xùn)練變式訓(xùn)練欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)方法技巧方法技巧欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)欄目欄目導(dǎo)引導(dǎo)引第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)第三章指數(shù)函數(shù)和對(duì)數(shù)函數(shù)失誤防范失誤防范要注意對(duì)數(shù)換底公式的特征：一個(gè)對(duì)數(shù)換為要注意對(duì)數(shù)換底公式的特