Bất đẳng thức ({log _{frac{2}{3}}}left( {frac{b}{3}} ight) < 0) đúng khi và chỉ khi

\(\begin{array}{l}{\log _{\frac{2}{a}}}\left( {\frac{b}{3}} \right) < 0 \Leftrightarrow \left[ \begin{array}{l}\left\{ \begin{array}{l}\frac{2}{a} < 1\\\frac{b}{3} > 1\end{array} \right.\\\left\{ \begin{array}{l}\frac{2}{a} > 1\\\frac{b}{3} < 1\end{array} \right.\end{array} \right.\\ \Leftrightarrow \left( {\frac{2}{a} - 1} \right)\left( {\frac{b}{3} - 1} \right) < 0 \Leftrightarrow \left( {2 - a} \right)\left( {b - 3} \right) < 0 \Leftrightarrow \left( {a - 2} \right)\left( {b - 3} \right) > 0\end{array}\)