《對(duì)數(shù)的概念》教學(xué) 課件

1、對(duì)數(shù)對(duì)數(shù)的概念與運(yùn)算對(duì)數(shù)函數(shù)1. 對(duì)數(shù)的概念 如果a(a0,a1)的b次冪等于N,即ab=N,那么就稱b是以a為底N的對(duì)數(shù),記作logaN=b.其中,a叫做對(duì)數(shù)的底數(shù),N叫做真數(shù),N0.lgN叫常用對(duì)數(shù), lnN叫自然對(duì)數(shù)2. 對(duì)數(shù)恒等式3. 對(duì)數(shù)的運(yùn)算性質(zhì)4. 換底公式對(duì)數(shù)對(duì)數(shù)的概念與運(yùn)算對(duì)數(shù)函數(shù)1. 對(duì)數(shù)的概念2. 對(duì)數(shù)恒等式 loga1=0 logaa=1 (其中a0,a1) a =N3. 對(duì)數(shù)的運(yùn)算性質(zhì)4. 換底公式對(duì)數(shù)對(duì)數(shù)的概念與運(yùn)算對(duì)數(shù)函數(shù)1. 對(duì)數(shù)的概念2. 對(duì)數(shù)恒等式3. 對(duì)數(shù)的運(yùn)算性質(zhì)4. 換底公式 loga(MN)=logaM+logaN loga =logaM-logaN

2、 loga =nlogaM其中a0,a1,M0,N0,nR對(duì)數(shù)對(duì)數(shù)的概念與運(yùn)算對(duì)數(shù)函數(shù)1. 對(duì)數(shù)的概念2. 對(duì)數(shù)恒等式3. 對(duì)數(shù)的運(yùn)算性質(zhì)4. 換底公式利用換底公式我們可以得到 其中a0,a1,c0,c1,N0 其中a0,a1,b0,b1 其中a0,a1,N0,n1 對(duì)數(shù)對(duì)數(shù)的概念與運(yùn)算對(duì)數(shù)函數(shù)1. 對(duì)數(shù)的概念2. 對(duì)數(shù)恒等式3. 對(duì)數(shù)的運(yùn)算性質(zhì)4. 換底公式對(duì)數(shù)函數(shù)的概念2. 對(duì)數(shù)函數(shù)的圖象和性質(zhì)對(duì)數(shù)對(duì)數(shù)的概念與運(yùn)算對(duì)數(shù)函數(shù)1. 對(duì)數(shù)的概念2. 對(duì)數(shù)恒等式3. 對(duì)數(shù)的運(yùn)算性質(zhì)4. 換底公式1. 對(duì)數(shù)函數(shù)的概念2. 對(duì)數(shù)函數(shù)的圖象和性質(zhì) 函數(shù)y=logax(a0,a1)叫做對(duì)數(shù)函數(shù),它的定義域

3、為(0,+)a10a1 在(0,+)上是 0a1 在(0,+)上是(0,+)R(1,0)單調(diào)增函數(shù)單調(diào)減函數(shù)夯實(shí)基礎(chǔ)一一、指數(shù)式與對(duì)數(shù)式互化(1) . (2) . (3) . (4) .(5) .二、常見(jiàn)對(duì)數(shù)求值log31= , log2 = , log327= ,lg1000= , lne2= , 2 = ,log2 = , = , lg2+lg5= ,log256-log27= , = .0-133232133-2=x(3) (4) log89log332(1) +(2)三、計(jì)算(1) 21-x=5,求x (2) log5log3(log2x)=0,求log16x(3) 已知lg2=a,l

4、g3=b,試用a,b表示 log512應(yīng)用與延伸夯實(shí)基礎(chǔ)二一、求下列函數(shù)的定義域(1) y=log3(2x-3) (2)夯實(shí)基礎(chǔ)二二、比較大小(1)log0.33 log0.32 (2) ln0.32 lg2(3) a=20.3,b=0.32,c= ,則 .bc一、求下列函數(shù)的定義域(1) y=log3(2x-3) (2)三、解不等式(1) 33-x6 (2) lg(x-1)1四、圖象的變換 已知f(x)=lgx的圖象,畫出下列函數(shù)的圖象,并指出與y=f(x)之間的關(guān)系.(1) y=f(-x) (2) y=-f(x) (3) y=f(x+1) (4)y=f(x)-2 (5) y=f(x) (6) y=f(x)應(yīng)用與延伸1. 求證:函數(shù)y=log 0.5(3x