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Câu hỏi: Số nghiệm của phương trình ${{\log }_{3}}\left( {{x}^{2}}+4x \right)+{{\log }_{\dfrac{1}{3}}}\left( 2x+3 \right)=0$ là
A. $0.$
B. $1.$
C. $3.$
D. $2.$
A. $0.$
B. $1.$
C. $3.$
D. $2.$
Ta có:
$\begin{aligned}
& {{\log }_{3}}\left( {{x}^{2}}+4x \right)+{{\log }_{\dfrac{1}{3}}}\left( 2x+3 \right)=0\Leftrightarrow {{\log }_{3}}\left( {{x}^{2}}+4x \right)-{{\log }_{3}}\left( 2x+3 \right)=0 \\
& \Leftrightarrow \left\{ \begin{aligned}
& 2x+3>0 \\
& {{x}^{2}}+4x=2x+3 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x>-\dfrac{3}{2} \\
& {{x}^{2}}+2x-3=0 \\
\end{aligned} \right.\Leftrightarrow x=1\left( TM \right) \\
\end{aligned}$
$\begin{aligned}
& {{\log }_{3}}\left( {{x}^{2}}+4x \right)+{{\log }_{\dfrac{1}{3}}}\left( 2x+3 \right)=0\Leftrightarrow {{\log }_{3}}\left( {{x}^{2}}+4x \right)-{{\log }_{3}}\left( 2x+3 \right)=0 \\
& \Leftrightarrow \left\{ \begin{aligned}
& 2x+3>0 \\
& {{x}^{2}}+4x=2x+3 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x>-\dfrac{3}{2} \\
& {{x}^{2}}+2x-3=0 \\
\end{aligned} \right.\Leftrightarrow x=1\left( TM \right) \\
\end{aligned}$
Đáp án B.