I've been trying to solve this non-linear equation for some time but to no avail. I've also tried Mathematica and Matlab. But I believe that a solution exists in terms of x (probably using the Lambert W function).

That's the equation below.

$ b cdot x ^ a + d cdot ln (1 + c cdot x) + ln (1+ (e ^ p-1) cdot (1-u)) / p = 0 $

Please, I would be grateful if the symbolic solution is in terms of x.

Thank you.