Đặt

B

- Hướng dẫn giải

Đáp án B

Ta có ${\log }_{15}10=\frac{{\log }_{5}10}{{\log }_{5}15}=\frac{{\log }_5\left(2.5\right)}{{\log }_5\left(3.5\right)}=\frac{{\log }_{5}2+1}{{\log }_{5}3+1}$ mà ${\log }_{5}3=\frac{1}{a}; {\log }_{5}2=\frac{{\log }_{5}4}{2}=\frac{1}{2b}$. 

Khi đó ${\log }_{15}10=\frac{{\displaystyle \frac{1}{2b}}+1}{{\displaystyle \frac{1}{a}}+1}=\frac{{\displaystyle \frac{2b+1}{2b}}}{{\displaystyle \frac{a+1}{a}}}=\frac{a\left(2b+1\right)}{2b\left(a+1\right)}=\frac{a+2ab}{2b+2ab}$.