Question

Решите логарифмическое неравенство

Answer 1

$log_{0,5}^2\, x+log_{0,5}\, x-2\ \textgreater \ 0\; \; ,\; \; \; ODZ:\; \underline {x\ \textgreater \ 0}\\\\t=log_{0,5}\, x\; \; ,\; \; \; t^2+t-2\ \textgreater \ 0\; \; ,\; \; \; t_1=-2,\; \; t_2=1\\\\(t-1)(t+2)\ \textgreater \ 0\; ,\; \; \; +++(-2)---(1)+++\\\\t\ \textless \ -2\; \; ili\; \; t\ \textgreater \ 1\\\\a)\; \; log_{0,5}\, x\ \textless \ -2\; \; ,\; \; log_{0,5}\, x\ \textless \ log_{0,5}(0,5)^{-2}\; ,\; \; x\ \textgreater \ (0,5)^{-2}\\\\x\ \textgreater \ (\frac{1}{2})^{-2}\; \; ,\; \; x\ \textgreater \ 2^2\; \; ,\; \; \underline {x\ \textgreater \ 4}\\\\b)\; \; log_{0,5}\, x\ \textgreater \ 1\; \; ,\; \; log_{0,5}\, x\ \textgreater \ log_{0,5}\, 0,5\; \; ,\; \; \underline {x\ \textless \ 0,5}\\\\Otvet:\; \; x\in (0;\,0,5)\cup (4,+\infty )\; .$