Question

Известно,что log5^3=m и log5^2=n.выразите через m и n значение log24^72

Answer 1

$log_53=m;$

$log_52=n;$

$log_{24}72=?$

$log_{24}72=\frac{log_{5}72}{log_{5}24}=$

$=\frac{log_{5}(8*9)}{log_{5}(8*3)}=\frac{log_{5}8+log_59}{log_{5}8+log_53}=$

$=\frac{log_{5}2^3+log_53^2}{log_{5}2^3+log_53}=$

$=\frac{3log_{5}2+2log_53}{3log_{5}2+log_53}=$

$=\frac{3n+2m}{3n+m}$