Finding roots of an exponential equation $16^{-x}=-log_{16}x$

Question

Is it possible to find all roots of this equation, without using an approximation(recursive) function like Newton's method? $$16^{-x}=-log_{16}x$$

Answer 1

The form of the equation makes one wonder whether there could be a simple solution of the form $x=2^{-\alpha}$. Converting the given equation into an equation for $\alpha$ and trying a few values then shows that $x={1\over4}$ is indeed a solution.