Решите, пожалуйста, неравенство log3^2x-log3x-2>0. Created by cherck2014. algebra-ru

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

cherck2014 @cherck2014

August 2022 1 7 Report

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

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

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