Normalizing an exponential function

Question

Given the equation $a^\frac yx + a^x=b$ is there a way to normalize this function into a form where $y=$...?

In short can I express $y$ in terms of $x$ if $a$ and $b$ are constants?

Answer 1

First rewrite to $a^{y/x}=b-a^x$, then take the $\log$ on both sides to get $\frac{y}{x}\log(a) = \log(b-a^x)$. Finally, we obtain $$y = x\frac{\log(b-a^x)}{\log(a)}.$$