Tập nghiệm \(S\) của bất phương trình \({\log _2} {x - 1} < 3\) là

4/22

Tập nghiệm \(S\) của bất phương trình \({\log _2}\left( {x - 1} \right) < 3\) là

\(S = \left( {1\,;\,9} \right)\).

\(S = \left( {1\,;\,10} \right)\).

\(S = \left( { - \infty \,;\,10} \right)\).

\(S = \left( { - \infty \,;\,9} \right)\).

Giải thích

\({\log _2}\left( {x - 1} \right) < 3\)\( \Leftrightarrow \left\{ \begin{array}{l}x - 1 > 0\\x - 1 < {2^3}\end{array} \right.\)\( \Leftrightarrow \left\{ \begin{array}{l}x > 1\\x < 9\end{array} \right. \Leftrightarrow 1 < x < 9\).

Vậy tập nghiệm là \(S = \left( {1\,;\,9} \right)\).