[latex]| log_{2}x-4|[/latex][latex]| больше = 3+1/(5-[latex]| log_{2}x-4|[/latex])

[latex]|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 \ 9\end{array}[/latex] [latex] \left[\begin{array}{ccc}0