对数的运算思考?;4log2log42log)1(222;16log4log164log)2(444==条件?如果成立需要满足什么是否恒成立,对于NMNMaaaloglog)(logNMNMaaaloglog)(log证明:证明思路:1.对数的定义,确定范围2.指数和对数关系,转化式子对数和指数的关系:当a>0,a≠1时,ax=Nx=logaNlogaN我们知道指数函数y=ax的值域是恒大于零的,所以N也就是大于零的。NMNMaaaloglog)(log证明:0,0,1a,0aNM且有条件证:根据对数的定义,,由于nmnmaaa,设nmaNa,M,nmaMN,由对数定义得nmNMnNma)(log,log,MlogaaNlogMlogN)(Mlogaaaam÷an=am-n01(am)n=amn02思考?这样我们就得到了对数运算的性质:).(loglog3;loglog)M(log2;loglog)(log1那0,>N0,>M,1≠a,且0>a如果nRnMnMNMNNMNMaaaaaaaa)()()(么:例1用logax、logay、logaz表示下列各式:32log2log1zyxzxyaa)(;)(解:zxyalog1)(zxyaalog)(logzyxaaalogloglog32log2zyxa)(32log)(logzyxaa31212logyloglogzxaaazxaaalog31ylog21log2例2求的值。5100lg解:5100lg52lg105210l52g回顾NMNMaaaloglog)(logNMNaaaloglog)M(log)(logMlogRnMnana感谢您的观看