§4.5.2对数的运算

§4.5.2对数的运算1.两个基本对数：(a＞0，且a≠1)底的对数等于1；1的对数等于0.logaa=1，loga1=02.对数运算法则：(其中a0，a1，M0，N0))(MNalogNMalognaMlogNMaaloglogNMaaloglogMnalog对数计算的依据2log)1(zxya例1若，用m、n、p表示下列各式：你试试？yzxalog)4()(log)3(53yxa解：2log)1(zxya32log)2(zyxapznymxaaalog,log,log2log)(logzxyaazyxaaalog2loglog32log)2(zyxa32log)(logzyxaazyxaaalog31log21log2pnm2pnm312129lg81lg)1(例2计算你试试？9log27log)3(55)2724091(log)2(3解：9lg81lg)1(9lg9lg29lg9lg22)2724091(log)2(327243log39log3233log2)8141(log)4(2例3计算你试试？解：(1)原式=2lg5lg2lg5lg)1(242log2112log487log)2(22218lg7lg37lg214lg)4(50lg2lg5lg)3(22lg)2lg5(lg5lg2lg10lg5lg2lg5lg10lg1(2)原式=42log)12487(log224212487log221log22122log21例4若，求x.0logloglog532x你试试？解：0logloglog532x1loglog53x3log5x35x1250logloglog245x若，求x.