Cho a=log2 15 thì P=log25 15 bằng ?

Đáp án A

Ta có $P={\log }_{25}15={\log }_{5^2}\left(5.3\right)=\frac{1}{2}({\log }_{5}5+{\log }_{5}3)=\frac{1}{2}+\frac{1}{2}{\log }_{5}3=\frac{1}{2}+\frac{1}{2{\log }_{3}5}$

Mà $a={\log }_{3}15={\log }_3\left(5.3\right)={\log }_{3}5+1\Rightarrow {\log }_{3}5=a-1$

Vậy $P={\log }_{25}15=\frac{1}{2}+\frac{1}{2(a-1)}=\frac{a}{2\left(a-1\right)}.$