对数的运算性质课件

1.对数的定义(a0a1,N0)且常用对数：自然对数：N10log=lgNNelog=lnN)100g100(log10l)6n6(logle2.对数的性质1)零和负数没有对数,即真数N＞0;2)1的对数是0,即;01loga3)底数的对数等于1,即;1logaa4)对数的恒等式.NaNalog5)对数的恒等式.)logRnnana（知识要点前提：如果a0,a≠1,M0,N0,则：(1)aaalog(MN)logMlogN;(2)aaaMloglogMlogN;N=-(3)naalogMnlogM(nR).积对数等于对数之和.商对数等于对数之差.幂对数等于n倍的对数.3.用表示下列各式.log,log,logaaaxyz2logloglogaaaxyz=++222(1)log()(2)log(3)logaaaxxxyzyzyz22(1)log()loglo:glogaaaaxyzxyz=++解3.用表示下列各式.log,log,logaaaxyz222(1)log()(2)log(3)logaaaxxxyzyzyz22(2)loglog(loglog)aaaaxxyzyz=-+2logloglogaaaxyz=--3.用表示下列各式.log,log,logaaaxyz3.用表示下列各式.222(1)log()(2)log(3)logaaaxxxyzyzyz22(3)loglog(loglog)aaaaxxyzyz=-+1log2loglog2aaaxyz=--log,log,logaaaxyz谈谈收获1.对数的运算性质前提：如果a0,a≠1,M0,N0,则：(1)aaalog(MN)logMlogN;推而广之：).,3,2,1,0logloglog)(g2121akNNNNNNNlokkaaak＞（).(logloggaMNNMloaa谈谈收获2.灵活运用对数的运算性质来解决实际问题.(2)aaaMloglogMlogN;N=-(3)naalogMnlogM(nR).).(loglog-gaNMNMloaa换底公式知识点5.换底公式)0,1,0,1,0(logloglogNbbaabNNaab三个较为常用的推论bmnbababbanabaamloglog)3(1loglog)2(lglglog)1(logab·logbc·logcd·logde=logae例：求log89·log2732的值；)2log4log8(log)5log25log125)(log3(625log9log)2(8log5log3log15251258422725532）（计算:知识点5.换底公式对数式有意义的条件).56(log)2();3(log)1(2712xxxxx[例3]求下列各式中x的取值范围：练一练