Задача 6А. Решите неравенство \({\log _{0,7}}\left( {2x + 1} \right) > 1\)
Ответ
ОТВЕТ: \(\left( {-0,5;-0,15} \right).\)
Решение
\({\log _{0,7}}\left( {2x + 1} \right) > 1\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\log _{0,7}}\left( {2x + 1} \right) > {\log _{0,7}}0,7\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{2x + 1 < 0,7,}\\{2x + 1 > 0\,\,\,\,\,\,}\end{array}\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{x < -0,15,}\\{x > -0,5\,\,\,}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x\, \in \,\,\left( {-0,5;-0,15} \right).} \right.\)
Ответ: \(\left( {-0,5;-0,15} \right).\)