Solution of $x+\log(x)=c$

Question

how to solve the following equation?

$x+\log(x)=n+c$,where $c$ is constant, and $n$ is positive number and allow to be infinity.

Intuitively, if let $n \to \infty$， the approximate solution will be $x=n+c-\log(n)$, can any one help with the exact solution?

Answer 1

you can write that as $x\log e+\log x=n+c$

$\log xe^x=n+c$

and now you x on one side and constants on another