对数函数的运算法则

对数运算法则一、对数的定义：对数blogNaNab底数真数注：负数和零没有对数01loga1logaaNaNalog(N0)babalog二、对数运算法则1、运算公式：a0,a≠1,M0;N0则：NaMaNMaloglog)(log①NaMaNMalogloglog②)(loglogRnMannMa③NaNalog∴M∙N=aq+pNaMalogloglogqpNMa证明：性质①设∴M=apN=aq∴M∙N=ap∙aq=aq+pqNapMaloglogNaMaNMalogloglog②练习：证明2、应用举例：例1、用表示下列各式：zayaxalog,log,logzxyalog)(1322zyxalog)(zayaxazaxyazxyaloglogloglog)(loglog)(1解：32322zayxazyxalogloglog)(32zayaxalogloglogxayaloglog3121xa2log3222224231)(log)()(logyxxyxayzxa）（算下列各式。练习：用对数的法则计(其中x0,y0,z0x-y0)例2：求下列各式的值：5100lg)2()(log52742（1）522742527421loglog(log））解：（19514225427loglog5100lg)2(5221051511001005lg)lg(lg271364232552logloglog练习：2533271315223)log(logloglog)(2325312533301)(log解：原式25502224lglglg))(lg(25105222lg)(lglg)(lg解：原式5215222lg)(lglg)(lg）（）（212221222210225222lglglglg)(lglglglglg)(lg2)(lglglglglg220583225(1)练习：计算14222112248722logloglog)(2NaMaNMaloglog)(log①NaMaNMalogloglog②)(loglogRnMannMa③）公式知识回顾：（1NaNalog:)(公式的作用2化简；求值；证明。