is there a closed formula for such an equation to find the value of $x$ in
$ax = b^x$
if there isn't , are there any published attempts ?
2026-04-02 18:45:08.1775155508
formula for equation with exponent variable?
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The solution of $ax = b^x$ is given by $$x=-\frac{W\left(-\frac{\log (b)}{a}\right)}{\log (b)}$$ where $W(z)$ is Lambert function such that $z=W(z)\,e^{W(z)}$.
It is a very interesting, fascinating, useful function with alot of partical applications.
Search on this site; you would find a lot of QA about it.