對(duì)數(shù)函數(shù)的運(yùn)算法則

1、 對(duì)數(shù)運(yùn)算法則對(duì)數(shù)運(yùn)算法則一、對(duì)數(shù)的定義：一、對(duì)數(shù)的定義：對(duì)數(shù)對(duì)數(shù)b bloglogn na an na ab b底數(shù)底數(shù)真數(shù)真數(shù)注：注： 負(fù)數(shù)和零沒(méi)有對(duì)數(shù)負(fù)數(shù)和零沒(méi)有對(duì)數(shù)01log a1log aanana log(n0)二、對(duì)數(shù)運(yùn)算法則二、對(duì)數(shù)運(yùn)算法則1 1、運(yùn)算公式：、運(yùn)算公式：a0, a1, m0;n0 a0, a1, m0;n0 則：則： namanmaloglog)(lognamanmalogloglog)(loglogrnmannmanana log m mn=an=aq+pq+pnamalogloglogqp nma證明：性質(zhì)證明：性質(zhì) 設(shè)設(shè) m=am=ap p n=an=aq

2、 q m mn=an=ap pa aq q=a=aq+pq+pqnapmaloglog namanmalogloglog練習(xí)：證明練習(xí)：證明2 2、應(yīng)用舉例：、應(yīng)用舉例： 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

3、下列列各各式式。練練習(xí)習(xí)：用用對(duì)對(duì)數(shù)數(shù)的的法法則則計(jì)計(jì)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練練習(xí)習(xí)：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) 練練習(xí)習(xí)：計(jì)計(jì)算算14222112248722logloglog)(namanmaloglog)(lognamanmalogloglog)(loglogrnmannma）公式）公式知識(shí)回顧：（知識(shí)回顧：（ 1nana lo