化简(log(2)(5)+log(4)(0.2))(log(5)(2)+log(25)(0.5))
问题描述：
化简(log(2)(5)+log(4)(0.2))(log(5)(2)+log(25)(0.5))
（还要追问,不懂的朋友请不要复制回答）
答
[log(2)(5)+log(4)(0.2)] [log(5)(2)+log(25)(0.5)]
=(lg5/lg2+lg0.2/2lg2) (lg2/lg5+lg0.5/2lg5)
=[(lg25+lg0.2)/2lg2] [(lg4+lg0.5)/2lg5
=(lg5/2lg2)(lg2/2lg5)
=1/4log(25)(0.5)请问上面的如何化成下面的ln(0.5)/2ln(5)log(25)(0.5)=lg0.5/2lg5=1/2log(5)(0.5)=(lg5/2lg2)(lg2/2lg5)=1/4这两部怎么化？=(lg5/2lg2)(lg2/2lg5)=(lg5xlg2)/4lg5xlg2)=1/4分子lg5xlg2与分母lg5xlg2约分