I have the equation x = a*b^x and want to solve it for x. But every online solver I tried says that it is not possible.
But when I choose a==8 and b==0.5 there is a solution for x==2
Is it not possible to solve the equation formally?
I have the equation x = a*b^x and want to solve it for x. But every online solver I tried says that it is not possible. But when I choose a==8 and b==0.5 there is a solution for x==2 Is it not possible to solve the equation formally? 


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There are no elementary formulas for such equations. Using the Lambert W function, the solution is $$x = \frac{W(a \log b)}{\log b}$$ 

