tex]

natfrance @natfrance

August 2022 1 8 Report

Решите неравенство
[tex]log_{2} (x-3) log_{2} (x-3) [/tex]<3

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NNNLLL54

Verified answer

$log_2(x-3)log_2(x-3)\ \textless \ 3\; ,\; \; ODZ:\; \; x\ \textgreater \ 3\\\\log^2_2(x-3)-3\ \textless \ 0\\\\(log_2(x-3)-\sqrt3)(log_2(x-3)+\sqrt3)\ \textless \ 0\\\\t=log_2(x-3)\; ,\; \; (t-\sqrt3)(t+\sqrt3)\ \textless \ 0\; \to \; \; -\sqrt3\ \textless \ t\ \textless \ \sqrt3\\\\ \left \{ {{log_2(x-3)\ \textgreater \ -\sqrt3} \atop {log_2(x-3)\ \textless \ \sqrt3}} \right. \; \left \{ {{x-3\ \textgreater \ 2^{-\sqrt3}} \atop {x-3\ \textless \ 2^\sqrt3}} \right. \; \left \{ {{x\ \textgreater \ 3+2^{-\sqrt3}} \atop {x\ \textless \ 3+2^{\sqrt3}}} \right. \\\\Otvet:\; \; x\in (3+2^{-\sqrt3};3+2^{\sqrt3}).$

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