Đáp án:30B; 31B
Giải thích các bước giải:
$\begin{array}{l}
30){\log _2}\left( {3x - 4} \right).{\log _2}x = {\log _2}x\left( 1 \right)\\
Đkxđ:\left\{ \begin{array}{l}
3x - 4 > 0\\
x > 0
\end{array} \right. \Rightarrow x > \frac{4}{3}\\
\left( 1 \right) \Leftrightarrow {\log _2}x\left( {1 - {{\log }_2}\left( {3x - 4} \right)} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
{\log _2}x = 0\\
{\log _2}\left( {3x - 4} \right) = 1
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 1\\
3x - 4 = 2
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 1\left( {ktm} \right)\\
x = 2\left( {tmdk} \right)
\end{array} \right.\\
\Rightarrow {x_1}^2 + {x_2}^2 = 5\\
\Rightarrow B\\
31)\\
{\log _2}x + 2{\log _5}x = 2 + {\log _2}x.{\log _5}x\left( {dkxd:x > 0} \right)\\
\Rightarrow \left( {{{\log }_2}x - 2} \right)\left( {1 - {{\log }_5}x} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
{\log _2}x = 2\\
{\log _5}x = 1
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 4\left( {tmdk} \right)\\
x = 5\left( {tmdk} \right)
\end{array} \right.\\
\Rightarrow {x_1}.{x_2} = 20\\
\Rightarrow B
\end{array}$
