Профиль №15. Логарифмические неравенства. Задача 14А

ОТВЕТ: \(\left( {0;16} \right].\)

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

\( \Leftrightarrow \,\,\,\,\,\,\,{\log _{0,25}}x \ge {\log _{0,25}}16\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{x \le 16,}\\{x > 0\,\,\,}\end{array}\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,x\, \in \,\left( {0;16} \right].} \right.\)

Ответ:  \(\left( {0;16} \right].\)