Cho \({a^{\frac{3}{4}}} > {a^{\frac{4}{5}}},{\r...

D

- Hướng dẫn giải

Phương pháp giải:

\({a^x} > {a^y} \Leftrightarrow \left[ \begin{array}{l}\left\{ \begin{array}{l}a > 1\\x > y\end{array} \right.\\\left\{ \begin{array}{l}0 < a < 1\\x < y\end{array} \right.\end{array} \right.;\,\,{\log _a}x > {\log _a}y \Leftrightarrow \left[ \begin{array}{l}\left\{ \begin{array}{l}a > 1\\x > y\end{array} \right.\\\left\{ \begin{array}{l}0 < a < 1\\x < y\end{array} \right.\end{array} \right.\)

Giải chi tiết:

Ta có

\(\begin{array}{l}\left\{ \begin{array}{l}\dfrac{3}{4} < \dfrac{4}{5}\\{a^{\frac{3}{4}}} > {a^{\frac{4}{5}}}\end{array} \right. \Rightarrow 0 < a < 1\\\left\{ \begin{array}{l}\dfrac{1}{2} < \dfrac{2}{3}\\{\log _b}\dfrac{1}{2} < {\log _b}\dfrac{2}{3}\end{array} \right. \Rightarrow b > 1\end{array}\)

Chọn D.