$\begin{align}  & {{\log }_{x}}8-{{\log }_{{{x}^{2}}}}16=1 \\ & {{\log }_{x}}{{2}^{3}}-\tfrac{1}{2}{{\log }_{x}}{{2}^{4}}=1\left| {{\log }_{{{a}^{n}}}}b=\tfrac{1}{n}{{\log }_{a}}b \right. \\ & 3{{\log }_{x}}2-\tfrac{4}{2}{{\log }_{x}}2=1 \\ & 3{{\log }_{x}}2-2{{\log }_{x}}2=1 \\ & {{\log }_{x}}2=1 \\ & {{x}^{1}}=2 \\ & x=2 \\\end{align}$