Question

Решите, , неравенство log3^2x-log3x-2> 0

Answer 1

$log_3^2x-log_3x-2\ \textgreater \ 0\; ,\; \; \; ODZ:\; \; x\ \textgreater \ 0\\\\t=log_3x7\; ,\; \; \; t^2-t-2\ \textgreater \ 0\; ,\; \; t_1=-1,\; \; t_2=2\\\\(t+1)(t-2)\ \textgreater \ 0\\\\+++(-1)---(2)+++\quad \left [ {{t\ \textless \ -1} \atop {t\ \textgreater \ 2}} \right. \; \; \left [ {{log_3x\ \textless \ -1} \atop {log_3x\ \textgreater \ 2}} \right. \; \; \left [ {{x\ \textless \ 3^{-1}} \atop {x\ \textgreater \ 3^2}} \right. \\\\Otvet:\; \; x\in (0 ,\frac{1}{3})\cup (9,+\infty )\; .$