7對(duì)數(shù)的概念與基本運(yùn)算

VIPEducatianVIPEducatian教肓皿EduoBtiDnVIP課程高一數(shù)學(xué)對(duì)數(shù)的概念與基本運(yùn)算1、 對(duì)數(shù)的概念一般地，若ax=N(a>0,且a豐1)，那么數(shù)x叫做以a為底N的對(duì)數(shù)，記作x=logNaa叫做對(duì)數(shù)的底數(shù)，N叫做真數(shù).2、 對(duì)數(shù)式與指數(shù)式的互化在對(duì)數(shù)的概念中，要注意：(1)底數(shù)的限制a>0,且a工1(2)ax二NologN二xa指數(shù)式o對(duì)數(shù)式幕底數(shù)一a-對(duì)數(shù)底數(shù)指數(shù)一x—對(duì)數(shù)幕 真數(shù)例1.將下列指數(shù)式化為對(duì)數(shù)式，對(duì)數(shù)式化為指數(shù)式.11(1)54=645 (2)2-6二 (3)G)m=5.7364 3(4)log16=—4 (5)log0.01=—2 (6)log10二2.30310 e2注：①以10為底的對(duì)數(shù)稱為常用對(duì)數(shù)，logN常記為lgN?10②以無(wú)理數(shù)e=2.71828…為底的對(duì)數(shù)稱為自然對(duì)數(shù)，logN常記為lnN.e例2：求下列各式中x的值2(1)logx=一 (2)log8二6 (3)lglOO=x(4)一lne2=x64 3 x3．歸納小結(jié)：對(duì)數(shù)的定義：ab=Nob=logN(a>0且a工1)a{1的對(duì)數(shù)是零，負(fù)數(shù)和零沒(méi)有對(duì)數(shù)log?二 1a>0且a工1aalogaN=N對(duì)數(shù)的運(yùn)算對(duì)數(shù)運(yùn)算是指數(shù)運(yùn)算的逆運(yùn)算logN二boab二N(a>0，且a工1，N>0)，a扌旨數(shù)的運(yùn)算性質(zhì)：am?an=am+n； amOan=am—n (am)n=amnM對(duì)數(shù)的運(yùn)算性質(zhì)：(1)logMN二logM+logN(2)log二logM—logNa a a aN a a(3)logMn二nlogM(neR)aa應(yīng)龜一1ZTP詼島間卅VIP課程高一數(shù)學(xué)讓護(hù)尋孚界眉正陽(yáng)壬他冊(cè)與屬棘目VIPEducatian例3.判斷下列式子是否正確，(a>0且a工1,x>0且x>y)1)logx-logy二log(x+y)(2)logx-logy二log(x-y)aaa3)log-二logxologyay(4)logxy二logx-logyaaa5)5)7)(logx)n二nlogxaanlogx二-logxa na(6)logx二一log-ax例4.計(jì)算：(1)log5(1)log535+2log丄、/2-log21550-log14⑵log8—log3—log_44 1 、'29例5?若lga、lgb是方程2x2-4x+1-0的兩個(gè)實(shí)根，求lg(ab)-(lgb)2的值?換底公式：若a>0,且a工1,c>0且cM1,b>0logb則logb=一alogac鞏固練習(xí)：1.將下列指數(shù)式與對(duì)數(shù)式互化，有x的求出x的值.1)51)5-2⑶3心2711⑷(衛(wèi)x二64(5)lg0.0001=x (6)lne5=x2.求aioga^iogbChgcN的值(a,b,ceR+,且不等于1,N>0)?3.計(jì)算3log/'5+73log35的值.4.用logx,logy,logz表示出(1)(2)小題，并求出(