How to solve a transcendental equation of the type $x^x = a$ with $a>0$, without leaving the solutions expressed in terms of the Lambert $W$ function?
For example the equation
$x^{x}=\left ( \frac{1}{3} \right )^{\frac{1}{4}}$
admit two solutions, how do I get to them by some method
I have applied the usual, but I don't see how to get to the result, any suggestions, some method, if possible with some steps to get started Thanks