Question

$log _{2} frac{8}{x} -log _{2} sqrt{2x}=-0.5$

Answer 1

$log_2 frac{8}{x} -log_2sqrt{2x}=-0,5; ;; ; ; ODZ:; ; x textgreater 0\\log_2frac{8}{xsqrt{2x}} =-frac{1}{2}\\frac{8}{sqrt2cdot x^{frac{3}{2}}}=2^{-frac{1}{2}}\\frac{8}{sqrt2cdot x^{frac{3}{2}}}=frac{1}{sqrt2}\\x^{frac{3}{2}}=2^3\\(sqrt{x})^3=2^3\\sqrt{x}=2; ; Rightarrow ; ; x=4$