Solving $xy + x\log x \geq z$ with respect to x. I have the inequality 
$xy+x\log x \geq z$
I would like solve this equation in with respect to $x$ and essentially 
rewrite the inquality above as 
$x \geq f(y,z)$.
What would be the simplest (and somewhat most accurate) $f$ that solves the problem above?

This is not a very simple equation to solve. You can get
$$x = \frac{z}{W(e^y z)}$$
with $W$ the lambert-$W$ function.
