Cho \(0<a<1\). Chọn khẳng...

D

- Hướng dẫn giải

Phương pháp giải:

\({\log _a}f\left( x \right) > {\log _a}g\left( x \right) \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
a > 1\\
0 < f\left( x \right) > g\left( x \right)
\end{array} \right.\\
\left\{ \begin{array}{l}
0 < a < 1\\
f\left( x \right) < g\left( x \right) > 0
\end{array} \right.
\end{array} \right.\)

Giải chi tiết:

\({\log _a}{x_1} < {\log _a}{x_2} \Rightarrow \left\{ \begin{array}{l}
0 < a < 1\\
{x_1} > {x_2} > 0
\end{array} \right. \Rightarrow A\) sai

\({\log _a}x < 1 = {\log _a}a \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
a > 1\\
0 < x < a
\end{array} \right.\\
\left\{ \begin{array}{l}
0 < a < 1\\
x > a > 0
\end{array} \right.
\end{array} \right. \Rightarrow B\) sai

\({\log _a}x > 0 = {\log _a}1 \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
a > 1\\
x > 1
\end{array} \right.\\
\left\{ \begin{array}{l}
0 < a < 1\\
0 < x < 1
\end{array} \right.
\end{array} \right. \Rightarrow C\) sai

Chọn D.