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Câu hỏi: Tập nghiệm của bất phương trình ${{\log }_{2}}\left( x+1 \right)-1>{{\log }_{2}}\left( 2x \right)$ là
A. $\left( -\infty ; \dfrac{1}{3} \right)$.
B. $\left( 0 ; \dfrac{1}{3} \right)$.
C. $\left( \dfrac{1}{3} ; +\infty \right)$.
D. $\left( -1 ; \dfrac{1}{3} \right)$.
${{\log }_{2}}\left( x+1 \right)-1>{{\log }_{2}}\left( 2x \right)$
$\Leftrightarrow \left\{ \begin{aligned}
& {{\log }_{2}}\left( \dfrac{x+1}{2} \right)>{{\log }_{2}}\left( 2x \right) \\
& x>0 \\
\end{aligned} \right.$
$\Leftrightarrow \left\{ \begin{aligned}
& x+1-4x>0 \\
& x>0 \\
\end{aligned} \right.$
$\Leftrightarrow \left\{ \begin{aligned}
& x<\dfrac{1}{3} \\
& x>0 \\
\end{aligned} \right.$.
A. $\left( -\infty ; \dfrac{1}{3} \right)$.
B. $\left( 0 ; \dfrac{1}{3} \right)$.
C. $\left( \dfrac{1}{3} ; +\infty \right)$.
D. $\left( -1 ; \dfrac{1}{3} \right)$.
${{\log }_{2}}\left( x+1 \right)-1>{{\log }_{2}}\left( 2x \right)$
$\Leftrightarrow \left\{ \begin{aligned}
& {{\log }_{2}}\left( \dfrac{x+1}{2} \right)>{{\log }_{2}}\left( 2x \right) \\
& x>0 \\
\end{aligned} \right.$
$\Leftrightarrow \left\{ \begin{aligned}
& x+1-4x>0 \\
& x>0 \\
\end{aligned} \right.$
$\Leftrightarrow \left\{ \begin{aligned}
& x<\dfrac{1}{3} \\
& x>0 \\
\end{aligned} \right.$.
Đáp án B.