[latex]log _{2} \frac{8}{x} -log _{2} \sqrt{2x}=-0.5 [/latex]

[latex]log_2 \frac{8}{x} -log_2\sqrt{2x}=-0,5\; ;\; \; \; ODZ:\; \; x\ \textgreater \ 0\\\\log_2\frac{8}{x\sqrt{2x}} =-\frac{1}{2}\\\\\frac{8}{\sqrt2\cdot x^{\frac{3}{2}}}=2^{-\frac{1}{2}}\\\\\frac{8}{\sqrt2\cdot x^{\frac{3}{2}}}=\frac{1}{\sqrt2}\\\\x^{\frac{3}{2}}=2^3\\\\(\sqrt{x})^3=2^3\\\\\sqrt{x}=2\; \; \Rightarrow \; \; x=4\\[/latex]