jmc

We begin by evaluating (or simplifying) the RHS of the equation. Since $2^4=16$, we know that ${\log }_{2}16=4$, so we have ${\log }_{x}81=4$. Writing this equation in exponential form, we get that $x^4=81$. This gives us the possible solutions $x=\pm 3$. However since the base of a logarithm is always positive, $x$ must equal $\boxed{3}$.