1、 对数运算法则对数运算法则.1一、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)babalog.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=a
2、N=aq q M MN=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
3、算下下列列各各式式。练练习习：用用对对数数的的法法则则计计(其中其中x0,y0,z0 x-y0).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 loglog.5100lg )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)(2.12NaMaNMaloglog)(logNaMaNMalogloglog)(loglogRnMannMa）公式）公式知识回顾：（知识回顾：（1NaNa log.13:)(公式的作用公式的作用2化简；求值；证明。化简；求值；证明。.14
