Giải bài 2.103; 2.104; 2.105 trang 137 - SBT Giải tích lớp 12

2.103.
\(\begin{aligned} & {{\left( \frac{1}{3} \right)}^{\frac{1}{x}}}<{{\left( \dfrac{1}{3} \right)}^{2}} \\ & \Leftrightarrow \dfrac{1}{x}>2\Leftrightarrow 0< x<\dfrac{1}{2} \\ \end{aligned} \)
Chọn C.
2.104.
 \(\begin{aligned} & \lg 2\left( x+1 \right)>1\,\,\,\,\,\,\,\,\,\,\, \\ & \Leftrightarrow \left\{ \begin{aligned} & x+1>0 \\ & 2\left( x+1 \right)>10 \\ \end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned} & x>-1 \\ & x+1>5 \\ \end{aligned} \right.\Leftrightarrow x>4 \\ \end{aligned} \)
Chọn A.
2.105. 
\(\begin{aligned} & {{\log }_{2}}\dfrac{3x}{x+2}>1 \\ & \Leftrightarrow \left\{ \begin{aligned} & \dfrac{3x}{x+2}>0 \\ & \dfrac{3x}{x+2}>2 \\ \end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned} & \left[ \begin{aligned} & x<-2 \\ & x>0 \\ \end{aligned} \right. \\ & \dfrac{x-4}{x+2}>0 \\ \end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned} & \left[ \begin{aligned} & x<-2 \\ & x>0 \\ \end{aligned} \right. \\ & \left[ \begin{aligned} & x<-2 \\ & x>4 \\ \end{aligned} \right. \\ \end{aligned} \right. \\ & \Leftrightarrow \left[ \begin{aligned} & x<-2 \\ & x>4 \\ \end{aligned} \right. \\ \end{aligned} \)

Chọn C.