$\begin{align}  & {{\log }_{{{x}^{\tfrac{1}{2}}}}}64=3 \\ & \text{Note: }{{\log }_{{{a}^{n}}}}b=\frac{1}{n}{{\log }_{a}}b \\ & \therefore {{\log }_{{{x}^{\tfrac{1}{2}}}}}64=\frac{1}{\tfrac{1}{2}}{{\log }_{x}}64=3 \\ & 2{{\log }_{x}}64=3 \\ & {{\log }_{x}}64=\frac{3}{2},{{x}^{\tfrac{3}{2}}}=64 \\ & x=\sqrt[3]{{{64}^{2}}}=\sqrt[3]{4096}=16 \\\end{align}$