## Solve $\ln(1-x)-\ln(x)+\frac{a}{x}=c$ for $x$

Is there an analytical (maybe involving special functions) solution of an equation of the form:

$$\ln(1-x)-\ln(x)+\frac{a}{x}=c$$

Here I want to solve for $$x$$, which should satisfy $$0\le x\le1$$, and $$a,c$$ are real constants.