1、 对数运算法则对数运算法则一、对数的定义：一、对数的定义：对数对数b bloglogN Na aN Na ab b底数底数真数真数注：注：负数和零没有对数负数和零没有对数01log a1log aaNaNa log(N0)二、对数运算法则二、对数运算法则1 1、运算公式：、运算公式：a0,a1,M0;N0 a0,a1,M0;N0 则：则：NaMaNMaloglog)(logNaMaNMalogloglog)(loglogRnMannMaNaNa log M MN=aN=aq+pq+pNaMalogloglogqp NMa证明：性质证明：性质 设设 M=aM=ap p N=aN=aq q M M
2、N=aN=ap pa aq q=a=aq+pq+pqNapMaloglog NaMaNMalogloglog练习：证明练习：证明2 2、应用举例：、应用举例：例例1 1、用、用 表示下列各式：表示下列各式：zayaxalog ,log ,logzxyalog)(132 2zyxalog)(zayaxazaxyazxyaloglogloglog)(loglog)(1解解：3232 2zayxazyxalogloglog)(32 zayaxalogloglogxayaloglog3121xa2log 322222 4231 )(log)()(logyxxyxayzxa）（算算下下列列各各式式。练练
3、习习：用用对对数数的的法法则则计计例例2 2：求下列各式的值：求下列各式的值：5100lg )2()(log52742（1）522742527421loglog(log）解解：（19514225427 loglog5100lg )2(5221051511001005lg)lg(lg271364232552logloglog练练习习：2533271315223)log(logloglog)(232531 2533301)(log解解：原原式式25502224lglglg)(lg(25105222lg)(lglg)(lg解解：原原式式5215222lg)(lglg)(lg）（）（212221222210225222lglglglg)(lglglglglg)(lg2)(lglglglglg220583225 (1)练练习习：计计算算14222112248722logloglog)(NaMaNMaloglog)(logNaMaNMalogloglog)(loglogRnMannMa）公式）公式知识回顾：（知识回顾：（1NaNa log:)(公式的作用公式的作用2化简；求值；证明。化简；求值；证明。.,.)(6 4 3 723 作作业业：习习题题
