Học lớp hướng dẫn giải
\(2{\log _2}(x - 1) \le {\log _2}(5 - x) \Leftrightarrow \left\{ \begin{array}{l} 5 > x > 1\\ {\log _2}{(x - 1)^2} \le {\log _2}2(5 - x) \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} 5 > x > 1\\ {(x - 1)^2} \le 2(5 - x) \end{array} \right.\)
\(\Leftrightarrow \left\{ \begin{array}{l} 5 > x > 1\\ {x^2} - 2x + 1 \le 10 - 2x \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} 5 > x > 1\\ {x^2} \le 9 \end{array} \right.\)
\(\Leftrightarrow \left\{ \begin{array}{l} 5 > x > 1\\ 3 \ge x \ge - 3 \end{array} \right. \Leftrightarrow 3 \ge x > 1 \Rightarrow S = (1;3].\)