100 БАЛЛОВ!!! Решите неравенство с логарифмами! Желательно с подробным решением!...

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100 БАЛЛОВ!!! Решите неравенство с логарифмами! Желательно с подробным решением!

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$x^2\cdot log_{16}x \geq log_{16}x^3+x\cdot log_2x\; ,\; \; \; ODZ:\; \; x\ \textgreater \ 0,\\\\x^2\cdot log_{2^4}x \geq log_{2^4}x^3+x\cdot log_2x\\\\x^2\cdot \frac{1}{4}\cdot log_2x-\frac{3}{4}\cdot log_2x-xlog_2x \geq 0\\\\log_2x\cdot (\frac{1}{4}x^2-x-\frac{3}{4}) \geq 0\; |\cdot 4\; \; \to \; \; \; log_2x\cdot (x^2-4x-3) \geq 0\\\\a) \left \{ {{log_2x \geq 0} \atop {x^2-4x-3 \geq 0}} \right. \; \left \{ {{x \geq 1} \atop {x\in (-\infty ,2-\sqrt7\, ]\cup [\, 2+\sqrt7,+\infty )}} \right. \; \; \to$

$x\in [\, 2+\sqrt7,+\infty )\\\\b)\; \; \left \{ {{log_2x \leq 0} \atop {x^2-4x-3 \leq 0}} \right. \; \left \{ {{x \leq 1} \atop {x\in [2-\sqrt7\, ;\, 2+\sqrt7\, ]}} \right. \; \to \; x\in [\, 2-\sqrt7\, ;1\, ]\\\\Otvet:\; \; x\in (0\, ;\, 1\, ]\cup [2+\sqrt7\, ;+\infty )$

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