I have a logarithmic equation: $u = A\left(\ln(u)+1\right)$. I used MATLAB's symbolic toolbox to solve this equation for
syms u A solve(u == A*log(u+1),u) ans = - A*wrightOmega(- log(-A) - 1/A) - 1
I looked up the Wright Omega function and wikipedia says it is defined by the Lambert W function. I was expecting the solution to the equation would have a Lambert W term. So, I am wondering if there is a relation that I can apply to write the solution with Lambert W instead of Wright Omega.