求值(log2 5+log4 1/5)(log5 2+log25 1/2)

问题描述:

求值(log2 5+log4 1/5)(log5 2+log25 1/2)

(log2 5+log4 1/5)(log5 2+log25 1/2)
=(log2 5-log4 5)(log5 2-log25 2)
=(lg5/lg2-lg5/lg4)(lg2/lg5-lg2/lg25)
=1/2lg5/lg2*1/2lg2/lg5
=1/4