人教版高一對(duì)數(shù)、指數(shù)的運(yùn)算練習(xí)及答案

1、對(duì)數(shù)的運(yùn)算公式，冪的運(yùn)算公式對(duì)數(shù)的運(yùn)算公式，冪的運(yùn)算公式.1.冪的有關(guān)概念:(1)正整數(shù)指數(shù)冪:=().(2)零指數(shù)冪:).nanN?01(aa??(3)負(fù)整數(shù)指數(shù)冪:.pa??(0)apN??(4)正分?jǐn)?shù)指數(shù)冪:mna?(0n1)amNn???且(5)負(fù)分?jǐn)?shù)指數(shù)冪:mna??(0n1)amNn???且(6)0的正分?jǐn)?shù)指數(shù)冪等于00的負(fù)分?jǐn)?shù)指數(shù)冪沒有意義.2.根式:(1)如果一個(gè)數(shù)的n次方等于a那么這個(gè)數(shù)叫做a的n次方根.??1nnN?

2、?且(2)0的任何次方根都是0記作.00n?(3)式子叫做根式n叫做根指數(shù)a叫做被開方數(shù).na(4).??nna?(5)當(dāng)n為奇數(shù)時(shí)=.(6)當(dāng)n為偶數(shù)時(shí)==.nnanna3.指數(shù)冪的運(yùn)算法則:(1)=.(2)=.rsaa?(0)arsR??rsaa(0)arsR??(3)=.(4)=.??rab(00)abrR?????sra(0)arsR??二.對(duì)數(shù)對(duì)數(shù)1.對(duì)數(shù)的定義:如果那么數(shù)b叫做以a為底N的對(duì)數(shù)記作(0baNa???且a1)其

3、中a叫做叫做真數(shù).2.對(duì)數(shù)的運(yùn)算法則:若那么0a??且a100MN??(1)=.(2)=.MNalogMNalog(3)=.nMalog3.特殊對(duì)數(shù):(1)=(2)=.(其中1alogaalog0a??且a1)4.對(duì)數(shù)的換底公式及對(duì)數(shù)恒等式(3)733338152aaaa????12a?變式訓(xùn)練1：化簡(jiǎn)93333271322aaaa????????????251212a?例2.化簡(jiǎn)132111333311111xxxxxxxx?????

4、????13x?變式訓(xùn)練2：化簡(jiǎn)(1)????????33334411aaaaaaaa??????????????1aa??(2)??111221xxxx???????????3322xx??題型二：對(duì)數(shù)式的運(yùn)算題型二：對(duì)數(shù)式的運(yùn)算例3.計(jì)算(log3)2－log0.259log5－1233log23?14523log2792變式訓(xùn)練3:化簡(jiǎn)或求值:(1)1??266661log3log2log18log4????????(2)4??2