Exact values of the equation $\ln (x+1)=\frac{x}{4-x}$ I'm asking for a closed form (an exact value) of the equation solved for $x$
$$\ln (x+1)=\frac{x}{4-x}$$
$0$ is trivial but there is another solution (approximately 2,2...).
I've tried with Lambert's W Function or with Regularized Gamma Functions but I didn't get so far.

Burniston and Siewert solved the equation:
$$ze^z=a(z+b)$$
Your equation can be reduced to the form:
$$5z-4= e^{z-1}z$$
which can be solved by Burniston Siewert integral
== References ==
[68] C. E. Siewert and E. E. Burniston, "Solutions of the Equation $ze^z=a(z+b)$," Journal of Mathematical Analysis and Applications, 46 (1974) 329-337. 
http://www4.ncsu.edu/~ces/pdfversions/68.pdf
