王強(qiáng)講的對(duì)數(shù)的運(yùn)算性質(zhì)

1、 主講人: 王強(qiáng)一、復(fù)習(xí)鞏固一、復(fù)習(xí)鞏固1、b = logaN（a0,a1,N0)2、等價(jià)式、等價(jià)式：ab=N logaN=b (a0,a1,N0) 3.對(duì)數(shù)恒等式對(duì)數(shù)恒等式（1）loga1=0(a0,且且a1)(2)logaa=1 (a0,且且a1)(3)logaab=b(a0,且且a1)（4）0, 1, 0logNaaNaNa且新授：對(duì)數(shù)的運(yùn)算法則 先回顧一下指數(shù)的運(yùn)算法則：nmnmaaanmnmaaamnnmaa)(二、對(duì)數(shù)運(yùn)算性質(zhì)二、對(duì)數(shù)運(yùn)算性質(zhì)探索探索：（1）logaM+logaN=?a0,a1, M0,N0成立MNNMaaalogloglog證明證明：由指數(shù)運(yùn)算法則得： NMaaa

2、qpqpqpMNa)(logNMMNaaaloglog)(log即：qNpMaalog,log，NaMaqp,則設(shè))6432(log) 1 (251log5log)2(333log2log)3(66做一做:116564log32log2201loglog3515316log32log66二、對(duì)數(shù)運(yùn)算性質(zhì)二、對(duì)數(shù)運(yùn)算性質(zhì)探索探索：a0,a1, M0,N0（2）logaM-logaN=?(3)logaMn=?MNNMaaalogloglog(1) 證明NMNMaaalogloglogNMaaaqpqpNMqpNMaaalogloglog由指數(shù)運(yùn)算法則得：qNpMaalog,logNaMaqp,證明

3、：設(shè)則成立loglognaaMnM證明證明：,logpMa,MappnnpnaaM)(MnManaloglog設(shè)則成立10010lg) 1 (2lg20lg)2(做一做:121100lg10lg10010lg110lg220lg2lg20lg110lg2lg2lg10lg2lg20lg110lg101lg10010lg1解解:二、對(duì)數(shù)運(yùn)算性質(zhì)二、對(duì)數(shù)運(yùn)算性質(zhì)（1）logaM+logaN=logaMN（2）logaM-logaN=NMalog(3) logaMn= nlogaM推論：推論：Ma1log1logMaMalogbaalogabalog=ba0,a1, M0,N0例例1、用、用loga

4、x,logay,logaz表示下列各式表示下列各式zxyalog) 1 (32log) 2(zyxazxyaaloglogzyxaaalogloglog32loglogzyxaa31212logloglogzyxaaazyxaaalog31log21log2 57224log1 5100lg21951415272log54log72log4log2252725210lg5210lg52求下列各式的值:計(jì)算下列各式的值計(jì)算下列各式的值100lg) 1 ()24(log) 2(572 5lg2lg)3(2lg50lg2lg25lg) 4 (25lg2lg35lg2lg) 5(33 注：注：lg2+lg5=1 lg