Question

Помогите1!! Решить неравенство​

Answer 1

$ODZ:\\1) \ x>0\\2) \ x\neq 0,5\\\\\\\log_{2x} 0,25\geq \log_{2} 32x-1\\\\\\\dfrac{\log_{2} 2^{-2} }{\log_{2} 2x} \geq \log_{2} 32+\log_{2} x-1\\\\\\\dfrac{-2}{1+\log_{2} x}\geq 5+\log_{2} x-1\\\\\\\log_{2} x=m\\\\\\\dfrac{-2}{1+m}-4-m\geq 0\\\\\\\dfrac{-2-4-4m-m-m^{2} }{1+m} \geq 0\\\\\\\dfrac{m^{2} +5m+6}{m+1} \leq 0\\\\\\\dfrac{(m+2)(m+3)}{m+1} \leq 0$

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$1) \ m\leq -3\\\\\log_{2} x\leq -3\\\\x\leq \dfrac{1}{8} \\\\\boxed{x\leq 0,125}\\\\\\2) \ -2\leq m<-1\\\\-2\leq \log_{2} x<-1\\\\\boxed{0,25\leq x<0,5}\\\\\\Otvet:\boxed{\Big(0 \ ; \ 0,125\Big] \ \cup \ \Big[0,25 \ ; \ 0,5\Big)}$