Помогите, пожалуйста, решить неравенство

$log_{2}0,5x \geq log_{16x}2* log_{4}16x^4; \\ log_{2}2^{-1}+ log_{2}x \geq \frac{1}{ log_{2}16+ log_{2}x}* (2log_{2}2+ 2log_{2}x); \\ log_{2}x-1 \geq \frac{2+2 log_{2}x }{4+ log_{2}x}; \\ log_{2}x=t; \\ t-1 \geq \frac{2+2t}{4+t}; \\ \frac{4t+t^2-4-t-2-2t}{4+t} \geq 0; \\ \frac{t^2+t-6}{4+t} \geq 0; \\ \frac{(t+3)(t-2)}{4+t} \geq 0; \\ -4\ \textless \ t \leq -3; \\ -4\ \textless \ log_{2}x \leq -3; \\ log_{2} \frac{1}{16}\ \textless \ log_{2}x \leq log_{2} \frac{1}{8}; \\$
$\frac{1}{16}\ \textless \ x \leq \frac{1}{8}; \\ t \geq 2; \\ log_{2}x \geq log_{2}4; \\ x \geq 4.$
ОДЗ:
x>0;
16x≠1;
x≠1/16.
Ответ: (1/16; 1/8]∪[4;+∞).