(Log5 2+ log2 5+2)*(log5 2-lg2)*log2 5-log5 2

Question

(Log5 2+ log2 5+2)*(log5 2-lg2)*log2 5-log5 2

Answer 1

Перейдем к основанию 2
(1/log(2)5+log(2)5+2)*(1/log(2)5 -1/(1+log(2)5)*log(2)5-1/log(2)5=
=(1+log²(2)5+2log(2)5)*(1+log(2)5-log(2)5)/[log(2)5*(1+log(2)5]*log(2)5-
1/log(2)5=(1+log(2)5)²/log(2)5*1/(1+log(2)5)-1/log(2)5=
=(1+log(2)5)/log(2)5-1/log(2)5=(1+log(2)5-1)/log(2)5=log(2)5/log(2)5=1