4.2.1 對(duì)數(shù)的概念課件高一上學(xué)期數(shù)學(xué)蘇教版（2019）必修第一冊(cè)

4.2.1對(duì)數(shù)的概念【學(xué)習(xí)目標(biāo)】

能夠在具體的數(shù)學(xué)情境中，得出對(duì)數(shù)的概念.知識(shí)點(diǎn)一對(duì)數(shù)的概念

底數(shù)真數(shù)

常用對(duì)數(shù)

自然對(duì)數(shù)

【診斷分析】1.判斷正誤.（請(qǐng)?jiān)诶ㄌ?hào)中打“√”或“×”）

×

×

×（4）對(duì)數(shù)運(yùn)算的實(shí)質(zhì)是求冪指數(shù).

()√2.（1）怎樣理解對(duì)數(shù)式的意義?

知識(shí)點(diǎn)二

對(duì)數(shù)的性質(zhì)與對(duì)數(shù)恒等式

1底數(shù)的對(duì)數(shù)等于101的對(duì)數(shù)等于00和負(fù)數(shù)2.對(duì)數(shù)恒等式為_(kāi)_________.

【診斷分析】判斷正誤.（請(qǐng)?jiān)诶ㄌ?hào)中打“√”或“×”）

×

×

×探究點(diǎn)一對(duì)數(shù)的概念例1（1）（多選題）下列說(shuō)法中正確的是(

)ACD

C

C

［素養(yǎng)小結(jié)］對(duì)數(shù)有意義的兩個(gè)條件：①底數(shù)大于0且不等于1；②真數(shù)必須大于0．探究點(diǎn)二指數(shù)式與對(duì)數(shù)式的互化例2

把下列各式中的對(duì)數(shù)式寫(xiě)成指數(shù)式，指數(shù)式寫(xiě)成對(duì)數(shù)式．

A

（2）（多選題）下列指數(shù)式與對(duì)數(shù)式互化正確的是(

)ABD

12

［素養(yǎng)小結(jié)］對(duì)數(shù)式與指數(shù)式的關(guān)系：由對(duì)數(shù)的定義知,對(duì)數(shù)式與指數(shù)式是同一種數(shù)量關(guān)系的兩種不同表達(dá)形式.其關(guān)系如下表:式子名稱意義

指數(shù)式

底數(shù)指數(shù)冪的次冪等于

對(duì)數(shù)式

底數(shù)對(duì)數(shù)真數(shù)以為底的對(duì)數(shù)等于

探究點(diǎn)三對(duì)數(shù)運(yùn)算例3

求下列各式的值.

2

探究點(diǎn)四利用對(duì)數(shù)性質(zhì)或?qū)?shù)恒等式求值例4（1）

求下列各式的值:

0

1

0

0

0

0

8

①②③

（1）對(duì)數(shù)的概念的實(shí)質(zhì)是指數(shù)式化為對(duì)數(shù)式，關(guān)鍵是弄清指數(shù)式各部分的“去向”：（2）對(duì)數(shù)的簡(jiǎn)單運(yùn)算可以利用指數(shù)式與對(duì)數(shù)式的關(guān)系或利用對(duì)數(shù)的性質(zhì)解決.1.（1）指數(shù)式化為對(duì)數(shù)式時(shí)，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)式時(shí)，將對(duì)數(shù)式的真數(shù)作為冪，對(duì)