Question

log1\9 (7-x) ⩾ -1\2. Решите неравенство.

Answer 1

$log_{ \frac{1}{9} } (7-x) \geq - \frac{1}{2} \\ \\ ODZ: 7-x\ \textgreater \ 0 \\ x\ \textless \ 7 \\ \\ - log_{9} (7-x) \geq - \frac{1}{2} \\ \\ l og_{9} (7-x) \leq \frac{1}{2 } \\ \\ log_{9} (7-x) \leq log_{9} 3 \\ \\ 9\ \textgreater \ 1 \\ \\ 7-x \ \leq 3 \\ \\ x \geq 4$

ОТВЕТ: x∈[4;7)