jmc

We can write ${\log }_2{x}^2=2{\log }_{2}x.$

By the change-of-base formula, $${\log }_{1/2}x=\frac{{\log }_{2}x}{{\log }_{2}1/2}=-{\log }_{2}x,$$so ${\log }_{2}x=5.$ Then $x=2^5=\boxed{32}.$