Cho

A

- Hướng dẫn giải

Đáp án A

Ta có ${\log }_{a^2}\left(\sqrt[3]{b^5{c}^4}\right)=\frac{1}{2}{\log }_a{\left(b^5{c}^4\right)}^{\frac{1}{3}}=\frac{1}{2}{\log }_a\left(b^{\frac{5}{3}}{c}^{\frac{4}{3}}\right)=\frac{1}{2}{\log }_a{b}^{\frac{5}{3}}+\frac{1}{2}{\log }_a{c}^{\frac{4}{3}}=\frac{5}{6}{\log }_{a}b+\frac{4}{6}{\log }_{a}c$

$=\frac{5}{6}.\frac{1}{{\log }_{b}a}+\frac{4{\log }_{b}c}{6{\log }_{b}a}=\frac{5}{6x}+\frac{4y}{6x}=\frac{5+4y}{6x}$