Question

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Answer 1

$\log_{ \frac{1}{3} }( \log_{2}(x^{2}-9) - 2) \geq-1\\ODZ:\\\left \{ {{\log_{2}(x^2-9)-20(1)} \atop {x^2-90 }} \right.\left \{ {{x\in(- \infty;-\sqrt{13})\cup(\sqrt{13};+ \infty)} \atop {x\in(- \infty;-3)\cup(3;+ \infty)}} \right.=x\in(- \infty;-\sqrt{13})\cup(\sqrt{13};+ \infty)\\(1)\\ \log_{2}(x^2-9)-20 \\\log_{2}(x^2-9)2 \\x^2-94=x\in(- \infty;-\sqrt{13})\cup(\sqrt{13};+ \infty)$

$\log_{2}(x^2-9)-2\leq \left(\frac{1}{3}\right)^{-1}\\\log_{2}(x^2-9)\leq 5\\x^2-9\leq 2^5\\x^2\leq 41\\x\in[-\sqrt{41};\sqrt{41}]$

Теперь накладываем ОДЗ и находим ответ

$x\in[-\sqrt{41};-\sqrt{13})\cup(\sqrt{13};\sqrt{41}]$