Solving for x in k=(x)ln(x): A Daunting Task

[Ja4Coltrane]

I was wondering how one would solve for x in the equation
k=(x)ln(x)

I tried all normal means. For example rewriting the equation with the x as an exponent of x. I have tried writing it in exponential form and the raising both sides to the power -k. I basically have no idea how to do this.
I do notice that the x sort of functions in the way that it would in a damping function...does that have anything to do with it?

 

[AlephZero]

Many "simple looking" equations, including your equation, do not have solutions that can be written as an explicit formula "x = something".

It is easy to solve the equation numerically, for any given value of k.

Of course the equations that occur in exercises all DO have solutions, and that might mislead you into thinking that any equation can be solved explicitly.