Профиль №15. Логарифмические неравенства. Задача 13А

ОТВЕТ: \(\left( {0;25} \right).\)

\(3{\log _{0,2}}x > -6\left| {:3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{{\log }_{0,2}}x > -2\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{{\log }_{0,2}}x > {{\log }_{0,2}}25\,\,\,\,\,\,\, \Leftrightarrow } \right.\)

\( \Leftrightarrow \,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{x < 25,}\\{x > 0\,\,\,}\end{array}\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,x\, \in \,\left( {0;25} \right).} \right.\)

Ответ:  \(\left( {0;25} \right).\)