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?



Problem solving equation of type x=a*b^x
There are no elementary formulas for such equations. Using the [Lambert W function](http://en.wikipedia.org/wiki/Lambert_W_function), the solution is $$x = -\frac{W(-a \log b)}{\log b}$$


