solution to $x=\log(x)+c$, not through numerical method

Question

I have got some equation $x=\log(x)+c$. Is there any particular solution to this(not with numerical methods)?

Thanks in advance.

Answer 1

Hint: $$x=\log x+ \log c$$ $$x=\log(xc)$$ $$10^x=xc$$

Answer 2

$x = - W(-e^{-c})$ where $W$ is any branch of the Lambert W function.