數(shù)學(xué)2.2.2-2對(duì)數(shù)與對(duì)數(shù)的運(yùn)算

2.2.1對(duì)數(shù)與對(duì)數(shù)運(yùn)算第二學(xué)時(shí)對(duì)數(shù)運(yùn)算1.定義:普通地，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.指數(shù)式與對(duì)數(shù)的關(guān)系:復(fù)習(xí)舊知識(shí)ax＝Nx＝logaN底數(shù)底數(shù)冪指數(shù)對(duì)數(shù)冪值真數(shù)0和負(fù)數(shù)沒(méi)有對(duì)數(shù)性質(zhì)1logal=0logaa=1性質(zhì)23.對(duì)數(shù)的性質(zhì)4.對(duì)數(shù)恒等式alogaN=N(a>0且a≠1)＋課前練習(xí)練習(xí)1:+練習(xí)2:求下列各式中x的值例:計(jì)算下列各式的值求下列三個(gè)對(duì)數(shù)的值：log232,log24,log28．新課思考:能否將log232＝log24十log28推廣到普通情形的結(jié)論？結(jié)論:loga（M·N）＝logaM十logaN(a>0，且a≠1，M>0，N>0)能證明嗎?你能發(fā)現(xiàn)這三個(gè)對(duì)數(shù)之間有哪些內(nèi)在聯(lián)系？1.對(duì)數(shù)的運(yùn)算性質(zhì)(1)loga（M·N）＝logaM十logaN如果a>0，且a≠1，M>0，N>0,那么冪的對(duì)數(shù)等于冪指數(shù)乘以底數(shù)的對(duì)數(shù)．兩數(shù)積的對(duì)數(shù)，等于各數(shù)的對(duì)數(shù)的和兩數(shù)商的對(duì)數(shù)，等于被除數(shù)的對(duì)數(shù)減去除數(shù)的對(duì)數(shù)2.性質(zhì)的應(yīng)用例3用logax，logay，logaz表示下列各式：分析:從真數(shù)的構(gòu)造進(jìn)行分解例2求下列各式的值：

(1)log2（47×25）；

(2)lg；(3)log318-log32；(4).提高練習(xí)1:求值

答案:1提高練習(xí)21.2.運(yùn)用立方和公式3.對(duì)數(shù)的運(yùn)算性質(zhì)(1)loga（M·N）＝logaM十logaN如果a>0，且a≠1，M>0，N>0,那么冪的對(duì)數(shù)等于冪指數(shù)乘以底數(shù)的對(duì)數(shù)．兩數(shù)積的對(duì)數(shù)，等于各數(shù)的對(duì)數(shù)的和兩數(shù)商的對(duì)數(shù)，等于被除數(shù)的對(duì)數(shù)減去除數(shù)的對(duì)數(shù)小結(jié)作業(yè)P74A3(5)(6