I have been trying to solve this nonlinear equation for sometime now to no avail. I have tried Mathematica and matlab as well. But I believe that a solution exist in terms of x (probably using the Lambert W function). This is 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 will be grateful if the solution $x$ is in term of other variables. Thank you.