Question

$| log_{2}x-4|$$|>= 3+1/(5-[tex]| log_{2}x-4|$)

Answer 1

$|log_2x-4| geq 3+ frac{1}{5-|log_2x-4|} \ |log_2x-4|=t \t geq 3+ frac{1}{5-t} \ frac{5t-t^2-15+3t-1}{5-t} geq 0 \ frac{t^2-8t+16}{t-5} geq 0 \ frac{(t-4)^2}{t-5} geq 0 \ t-5 textgreater 0 \ t textgreater 5\ |log_2x-4| textgreater 5 \ left[begin{array}{ccc}log_2x textless -1\log_2x textgreater 9end{array}$
$left[begin{array}{ccc}0<x textless frac{1}{2} \x textgreater 512end{array}$
x ∈ (0; 1/2) ∪ (512; +∞)