4.2.1對(duì)數(shù)的運(yùn)算性質(zhì)課件高一上學(xué)期數(shù)學(xué)北師大版

對(duì)的運(yùn)算性質(zhì)北師大版（2019）高中數(shù)學(xué)必修第一冊(cè)第四章

對(duì)數(shù)運(yùn)算與對(duì)數(shù)函數(shù)第2節(jié)

對(duì)數(shù)的運(yùn)算1.對(duì)數(shù)的定義底數(shù)對(duì)數(shù)真數(shù)溫故知新

其中a叫做底數(shù)，N叫做真數(shù)。

溫故知新2.對(duì)數(shù)的性質(zhì)1)零和負(fù)數(shù)沒(méi)有對(duì)數(shù),即真數(shù)N＞0;2)1的對(duì)數(shù)是0,即;3)底數(shù)的對(duì)數(shù)等于1,即;4)對(duì)數(shù)的恒等式.3.兩類(lèi)特殊的對(duì)數(shù)(1)以10為底的對(duì)數(shù)叫做常用對(duì)數(shù)，并把log10N記為lgN；(2)以無(wú)理數(shù)e＝2.71828…為底的對(duì)數(shù)稱(chēng)為自然對(duì)數(shù)，并把logeN記為lnN.例如：log109=lg9,log105=lg5,log10N=lgN等等例如：loge9=ln9,loge5=ln5,logex=lnx等等溫故知新4.對(duì)數(shù)與指數(shù)的互相轉(zhuǎn)化指數(shù)對(duì)數(shù)冪底數(shù)真數(shù)溫故知新5.指數(shù)冪的運(yùn)算性質(zhì)

對(duì)數(shù)源于指數(shù)，我們已經(jīng)知道對(duì)數(shù)和指數(shù)式怎樣互化的，指數(shù)與對(duì)數(shù)都是一種運(yùn)算，而且它們互為逆運(yùn)算，指數(shù)運(yùn)算有一系列性質(zhì)，那么對(duì)數(shù)運(yùn)算有那些性質(zhì)呢？是巧合么？還是有什么規(guī)律？上邊的結(jié)論，

用字母怎樣表示？課堂引導(dǎo)對(duì)數(shù)運(yùn)算性質(zhì)一一設(shè)二算三轉(zhuǎn)化課堂引導(dǎo)對(duì)數(shù)運(yùn)算性質(zhì)二一設(shè)二算三轉(zhuǎn)化對(duì)數(shù)的運(yùn)算性質(zhì)如果a>0,a

1,

M>0,N>0,則(1)(2)積的對(duì)數(shù)等于對(duì)數(shù)的和；商的對(duì)數(shù)等于對(duì)數(shù)的差;語(yǔ)言表達(dá):同底對(duì)數(shù)相加,底數(shù)不變,真數(shù)相乘.同底對(duì)數(shù)相減,底數(shù)不變,真數(shù)相除.返回課堂引導(dǎo)對(duì)數(shù)運(yùn)算性質(zhì)三一設(shè)二算三轉(zhuǎn)化對(duì)數(shù)的運(yùn)算性質(zhì)三如果a>0,a

1,

M>0,N>0,則(3)語(yǔ)言表達(dá):冪的對(duì)數(shù)等于對(duì)數(shù)的倍數(shù)；對(duì)數(shù)的倍數(shù)可以作為真數(shù)的指數(shù)；返回對(duì)數(shù)的運(yùn)算性質(zhì)如果a>0,a

1,

M>0,N>0,則(1)(2)(3)積的對(duì)數(shù)等于對(duì)數(shù)的和；商的對(duì)數(shù)等于對(duì)數(shù)的差;語(yǔ)言表達(dá):冪的對(duì)數(shù)等于對(duì)數(shù)的倍數(shù)；同底對(duì)數(shù)相加,底數(shù)不變,真數(shù)相乘.同底對(duì)數(shù)相減,底數(shù)不變,真數(shù)相除.對(duì)數(shù)的倍數(shù)可以作為真數(shù)的指數(shù)；返回思考交流①簡(jiǎn)易語(yǔ)言表達(dá)：“積的對(duì)數(shù)=對(duì)數(shù)的和”“商的對(duì)數(shù)=對(duì)數(shù)的差”“冪的對(duì)數(shù)=對(duì)數(shù)的倍數(shù)”.②注意公式的逆用.③真數(shù)的取值范圍必須是④對(duì)公式容易錯(cuò)誤記憶，要特別注意：說(shuō)明：解：小結(jié)：將積(商)的對(duì)數(shù)拆成同底的兩個(gè)對(duì)數(shù)的和(差)，即公式的正用；記為“拆”例2求下列各式的值：

(1)lg5＋lg2；(3)log35－log315.(1)lg5＋lg2＝lg(5×2)＝lg10＝1.解:總結(jié):對(duì)數(shù)的化簡(jiǎn)求值一般是正用或逆用公式，對(duì)真數(shù)進(jìn)行處理，選哪種策略化簡(jiǎn)，

取決于問(wèn)題的實(shí)際情況，一般本著便于真數(shù)化簡(jiǎn)的原則進(jìn)行.小結(jié)：將同底的兩個(gè)對(duì)數(shù)的和(差)合并為積(商)的對(duì)數(shù)，即公式逆用；記為“收”解：22解法一：解法二：靈活運(yùn)用三個(gè)公式，注意公式的正用和逆用.

提升練習(xí)計(jì)算：22計(jì)算：解

提升練習(xí)對(duì)數(shù)的運(yùn)算法則如果a>0,a

1,

M>0,N>0,則(1)(2)(3)積的對(duì)數(shù)等于對(duì)數(shù)的和；商的對(duì)數(shù)等于對(duì)數(shù)的差;語(yǔ)言表達(dá):冪的對(duì)數(shù)等于對(duì)數(shù)的倍數(shù)；同底對(duì)數(shù)相加,底數(shù)不變,真數(shù)相乘.同底對(duì)數(shù)相減,底數(shù)不變,真數(shù)相除.對(duì)數(shù)的倍數(shù)可以作為真數(shù)的指數(shù)；返回1.總結(jié)知識(shí)點(diǎn)：

2.總結(jié)解題方法對(duì)于底數(shù)相同的對(duì)數(shù)式的化簡(jiǎn)、求值,常用的方法是:(1)“收”,將同底的兩個(gè)對(duì)數(shù)的和(差)收成積(商)的對(duì)數(shù);(2)