(log(2)125+log(2)25+log(8)5)*(log(125)2+log(25)4+log(5)8)
问题描述：
(log(2)125+log(2)25+log(8)5)*(log(125)2+log(25)4+log(5)8)
答
(log(2)125+log(2)25+log(8)5)*(log(125)2+log(25)4+log(5)8)
=[3log2 5+2log2 5 +(log2 5)3]*[(log5 2)/3+log5 2+3log5 2]
=[(16log2 5)/3]*[(13log5 2)/3]
=208/9
答
=(lg125/lg2+lg25/lg2+lg5/lg8)(lg2/lg125+lg4/lg25+lg8/lg5)=(3lg5/lg2+2lg5/lg2+lg5/3lg2)(lg2/3lg5+2lg2/2lg5+3lg2/lg5)=(3+2+1/3)*(lg5/lg2)*(1/3+1+3)*(lg2/lg5)=16/3*13/3=208/9