Hey dude, Solving in tems of a Lamberts function is not an analytical solution. If you get the answer in terms of a Lamberts function, you then have to solve the Lamberts function numerically agian. Let me explain why you cannot get an absolute analytical solution of that equaiton. To solve that equation one should be able to collect x in a place. You just cannot do it if you have log(x) or e^x or 2^x and x together i none equation. Why? because for example log(1+x)=x-x^2/2+x^3/3........and similar expansions for e^x and 2^x. It is impossible to extract x analytically to solve it analytically. You have to use some function like Lamberts or solve it numerically. Hope I made my point clear. Implementation of this in Matlab is easy.