Google
Câu hỏi: Bất phương trình ${{3}^{2\text{x}+1}}-{{7.3}^{x}}+2>0$ có nghiệm
A. $\left[ \begin{aligned}
& x<-1 \\
& x>{{\log }_{2}}3 \\
\end{aligned} \right. $
B. $ \left[ \begin{aligned}
& x<-2 \\
& x>{{\log }_{2}}3 \\
\end{aligned} \right. $
C. $ \left[ \begin{aligned}
& x<-1 \\
& x>{{\log }_{3}}2 \\
\end{aligned} \right. $
D. $\left[ \begin{aligned}
& x<-2 \\
& x>{{\log }_{3}}2 \\
\end{aligned} \right.$
A. $\left[ \begin{aligned}
& x<-1 \\
& x>{{\log }_{2}}3 \\
\end{aligned} \right. $
B. $ \left[ \begin{aligned}
& x<-2 \\
& x>{{\log }_{2}}3 \\
\end{aligned} \right. $
C. $ \left[ \begin{aligned}
& x<-1 \\
& x>{{\log }_{3}}2 \\
\end{aligned} \right. $
D. $\left[ \begin{aligned}
& x<-2 \\
& x>{{\log }_{3}}2 \\
\end{aligned} \right.$
Bất phương trình tương đương với: ${{3.3}^{2\text{x}}}-{{7.3}^{x}}+2>0$
$\Leftrightarrow \left[ \begin{aligned}
& {{3}^{x}}<\dfrac{1}{3} \\
& {{3}^{x}}>2 \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& x<{{\log }_{3}}\dfrac{1}{3} \\
& x>{{\log }_{3}}2 \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& x<-1 \\
& x>{{\log }_{3}}2 \\
\end{aligned} \right.$
$\Leftrightarrow \left[ \begin{aligned}
& {{3}^{x}}<\dfrac{1}{3} \\
& {{3}^{x}}>2 \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& x<{{\log }_{3}}\dfrac{1}{3} \\
& x>{{\log }_{3}}2 \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& x<-1 \\
& x>{{\log }_{3}}2 \\
\end{aligned} \right.$
Đáp án C.