2025年高考數(shù)學(xué)一輪復(fù)習(xí)-4.3.1-對(duì)數(shù)的概念【課件】

第四章指數(shù)函數(shù)與對(duì)數(shù)函數(shù)4.3對(duì)數(shù)4.3.1對(duì)數(shù)的概念01預(yù)習(xí)案自主學(xué)習(xí)02探究案講練互動(dòng)03自測(cè)案當(dāng)堂達(dá)標(biāo)04應(yīng)用案鞏固提升學(xué)習(xí)指導(dǎo)核心素養(yǎng)1.會(huì)用對(duì)數(shù)的定義進(jìn)行對(duì)數(shù)式與指數(shù)式的互化．2.理解和掌握對(duì)數(shù)的性質(zhì)，會(huì)求簡(jiǎn)單的對(duì)數(shù)值．1.數(shù)學(xué)抽象：理解對(duì)數(shù)的概念，掌握對(duì)數(shù)的基本性質(zhì)，理解常用對(duì)數(shù)和自然對(duì)數(shù)的定義形式以及在科學(xué)實(shí)踐中的應(yīng)用．2.數(shù)學(xué)運(yùn)算：掌握指數(shù)式與對(duì)數(shù)式的互化，能夠應(yīng)用對(duì)數(shù)的定義和性質(zhì)解方程．1．對(duì)數(shù)的概念一般地，如果ax＝N(a>0，且a≠1)，那么數(shù)x叫做_________________，記作x＝________，其中a叫做對(duì)數(shù)的______，N叫做______．2．常用對(duì)數(shù)與自然對(duì)數(shù)以a為底N的對(duì)數(shù)logaN底數(shù)真數(shù)3．對(duì)數(shù)式與指數(shù)式的關(guān)系

4．對(duì)數(shù)的結(jié)論(1)______和___沒(méi)有對(duì)數(shù)．(2)loga1＝___(a＞0，且a≠1).(3)logaa＝___(a＞0，且a≠1).負(fù)數(shù)001(2)若a＝0，且N≠0，則logaN不存在；若a＝0，N＝0，log00有無(wú)數(shù)個(gè)，不能確定．為此，規(guī)定a≠0，N≠0.(3)若a＝1，且N≠1，則logaN不存在；若a＝1，N＝1，logaN有無(wú)數(shù)個(gè)值,不能確定．為此，規(guī)定a≠1.因此，為了避免對(duì)數(shù)logaN不存在或不唯一確定的情況，規(guī)定a>0，且a≠1.2．任何一個(gè)指數(shù)式都可以化為對(duì)數(shù)式嗎？提示：不是，如(－3)2＝9，不能寫(xiě)成log(－3)9＝2.1．判斷正誤(正確的打“√”，錯(cuò)誤的打“×”)(1)對(duì)數(shù)log39和log93的意義一樣．(

)(2)(－2)3＝－8可化為log(－2)(－8)＝3.(

)(3)對(duì)數(shù)式的實(shí)質(zhì)是求冪指數(shù)．(

)××√2．若a2＝M(a＞0，且a≠1)，則有(

)A．log2M＝a B．logaM＝2C．loga2＝M D．log2a＝M√3．把對(duì)數(shù)式loga49＝2寫(xiě)成指數(shù)式為(

)A．a(chǎn)49＝2 B．2a＝49C．492＝a D．a(chǎn)2＝49√講練互動(dòng)指數(shù)式與對(duì)數(shù)式互化的思路(1)指數(shù)式化為對(duì)數(shù)式：將指數(shù)式的冪作為真數(shù)，指數(shù)作為對(duì)數(shù)，底數(shù)不變，寫(xiě)出對(duì)數(shù)式．(2)對(duì)數(shù)式化為指數(shù)式：將對(duì)數(shù)式的真數(shù)作為冪，對(duì)數(shù)作為指數(shù)，底數(shù)不變，寫(xiě)出指數(shù)式．

求對(duì)數(shù)式logaN(a>0，且a≠1，N>0)的值的步驟(1)設(shè)logaN＝m.(2)將logaN＝m寫(xiě)成指數(shù)式am＝N.(3)將N寫(xiě)成以a為底的指數(shù)冪N＝ab，則m＝b，即logaN＝b.

√√3．若a>0，且a≠1，c>0，則將ab＝c化成對(duì)數(shù)式為(

)A．logab＝c