求(log2 5+log4 0.2)(log5 2+log25 0.5)

求(log2 5+log4 0.2)(log5 2+log25 0.5)
求(log2 5+log4 0.2)(log5 2+log25 0.5)

求(log2 5+log4 0.2)(log5 2+log25 0.5)
(log2 5+log4 0.2)(log5 2+log25 0.5)
=log2 5*log5 2+log5 2*log4 0.2+log2 5*log25 0.5+log4 0.2*log25 0.5)
=1-1/2-1/2+1/4=1/4

(log2 5+log4 0.2)(log5 2+log25 0.5)
=log2 5*log5 2+log2 5*log25 0.5+log4 0.2*log5 2+log4 0.2*log25 0.5
=lg5/lq2*lg2/lg5+lg5/lg2*lg0.5/lg25+lg0.2/lg4*lg2/lg5+lg0.2/lg4*lg0.5/lg25
=1-1/2-1/2+1/4
=1/4

(log2 5+log4 0.2)(log5 2+log25 0.5)
=(log2 5 + 0.5log2 0.2)(log5 2 + 0.5log5 0.5)
=(log2 5 + log2 0.1)(log5 2 + log5 0.25)
=log2 0.5 * log5 0.5
=-1 * (-log5 2)
=log5 2