Question

Помогите, пожалуйста, решить неравенство

Answer 1

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