
人教高中數(shù)學(xué)A版必修一《對(duì)數(shù)的概念》指數(shù)函數(shù)與對(duì)數(shù)函數(shù)PPT課件下載,共33頁。
課標(biāo)闡釋
1.理解對(duì)數(shù)的概念,掌握對(duì)數(shù)的基本性質(zhì).(數(shù)學(xué)抽象)
2.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.(數(shù)學(xué)運(yùn)算)
3.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.(數(shù)學(xué)抽象)
知識(shí)點(diǎn)一:對(duì)數(shù)的概念
1.對(duì)數(shù)的定義:一般地,如果ax=N(a>0,且a≠1),那么數(shù)x叫做以a為底N的對(duì)數(shù),記作x=logaN ,其中a叫做對(duì)數(shù)的底數(shù),N叫做真數(shù).
2.兩種特殊的對(duì)數(shù):
知識(shí)點(diǎn)二:對(duì)數(shù)的基本性質(zhì)
1.對(duì)數(shù)與指數(shù)間的關(guān)系
(1)當(dāng)a>0,a≠1時(shí),ax=N⇔x=logaN.
(2)對(duì)數(shù)恒等式:=N.
2.對(duì)數(shù)的基本性質(zhì)
(1)負(fù)數(shù)和零沒有對(duì)數(shù).
(2)對(duì)于任意的a>0,且a≠1,都有l(wèi)oga1=0,logaa=1,
loga=-1.
名師點(diǎn)析 1.對(duì)數(shù)恒等式的特點(diǎn):(1)指數(shù)中含有對(duì)數(shù)形式;(2)同底,即冪底數(shù)和對(duì)數(shù)的底數(shù)相同;(3)其值為對(duì)數(shù)的真數(shù).
2.loga1=0,logaa=1可簡述為“1的對(duì)數(shù)等于0,底的對(duì)數(shù)等于1”.
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