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Câu hỏi: Bất phương trình ${{\log }_{2}}\left( 3x-2 \right)>{{\log }_{2}}\left( 6-5x \right)$ có tập nghiệm là
A. $\left( \dfrac{1}{2};3 \right)$.
B. $\left( -3;1 \right)$.
C. $\left( 0;+\infty \right)$.
D. $\left( 1;\dfrac{6}{5} \right)$.
A. $\left( \dfrac{1}{2};3 \right)$.
B. $\left( -3;1 \right)$.
C. $\left( 0;+\infty \right)$.
D. $\left( 1;\dfrac{6}{5} \right)$.
${{\log }_{2}}\left( 3x-2 \right)>{{\log }_{2}}\left( 6-5x \right)\Leftrightarrow \left\{ \begin{aligned}
& 3x-2>0 \\
& 6-5x>0 \\
& 3x-2>6-5x \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& \dfrac{2}{3}<x<\dfrac{6}{5} \\
& x>1 \\
\end{aligned} \right.\Leftrightarrow 1<x<\dfrac{6}{5}$.
& 3x-2>0 \\
& 6-5x>0 \\
& 3x-2>6-5x \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& \dfrac{2}{3}<x<\dfrac{6}{5} \\
& x>1 \\
\end{aligned} \right.\Leftrightarrow 1<x<\dfrac{6}{5}$.
Đáp án D.