Cho log5(2)=m, log3(5)=n . Tính A= log25(2000)+log9(675) theo m,n .

* Hướng dẫn giải

Đáp án A

$A={\log }_{25}2000+{\log }_{9}675={\log }_{5^2}\left(5^3{.2}^4\right)+{\log }_{3^2}\left(3^3{.5}^2\right)$

$=\frac{3}{2}{\log }_{5}5+\frac{4}{2}{\log }_{5}2+\frac{3}{2}{\log }_{3}3+\frac{2}{2}{\log }_{3}5$

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