1102高一【数学(人教B版)】对数运算法则-课件(1).pptxVIP免费

对数运算法则高一年级数学主讲人孙天鸣北京师范大学附属中学北京市中小学空中课堂1的对数为0，底的对数为1.log10log1aaa底数的幂指数次方的对数为幂指数.logbaablogaNaN...对数的性质问题一：6log3你知道与的值吗？6log36log2你能算出的值吗？66log3+log2()mnmnmmmaaaabab公式前后哪些变了，哪些不变？666log3log2log(32)666log3log2log(32)还是？6log366log3,log2xy设则.63,62xy1xy+1666326xyxy666log3log2log(32)1，..积的对数6log3则0,0aMaN设log,logaaMNaaaMN由log()aMN知log()loglogaaaMNMN例1已知且，0a1,,0aMN证明:.logloglog()aaaMNMN，.，..log()loglogaaaMNMN积的对数对数运算法则：两个正因数积的对数等于同一底数的各因数对数的和.0,1,0,0aaMN其中，.问题二：6log3真数为有限多个正因数相乘时是否还成立？123123log()=log[()]aaNNNNNN123log()logaaNNN123log+loglogaaaNNN123123loglog+loglogaaaaNNNNNN1212log...loglog....log（）akaaakNNNNNNloglogkaaNkNk...，.幂的对数问题三：6log3aM设，则.logaMloglog()logaaaMaaloglogaaMM对于幂指数是任意实数是否成立呢？..()R幂的对数对数运算法则：正数幂的对数等于幂的底数的对数乘以幂指数.0,1,0，aaM其中.，loglogaaMM()RR商的对数6log311loglog()loglogloglogaaaaaaMMNMNMNN.商的对数对数运算法则：两个正数商的对数等于同一底数的被除数与除数的对数的差.logloglogaaaMMNN其中.0,1,0,0aaMN，积、幂、商的对数对数运算法则：6log3log()loglogaaaMNMNloglogaaMMlogloglogaaaMMNN0,1,0,0,aaMN其中，，，.R积、幂、商的对数6log3(1)logaxyzloglog,log，aaaxyz23logaxyz用表示下式.例2解:.1212323log=log（）aaxyxyzz11232logloglog=aaaxyz112logloglog23aaaxyz.积、幂、商的对数例3计算下式的值.6log3752log(42).解:7575222log(42)log4log2227log45log2725119.问题四：6log3lg3,lg53log5能否借助的值算出的值呢？3log51lg3,lg510预估，而.3log5lg3lg5能不能呢？3lg5log5lg3只能.3log5再来看看怎么办？换底公式6log33lg50.6990log51.4651lg30.4771...