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# Can you rearrange for $$x$$?

We have an equation $$y=x^{x^x}$$. Can we rearrange for $$x$$?

So far I have managed to get it close to a form where the Lambert-W Function can be used.

$\frac{\log y}{x^{x-1}}\exp\left({\displaystyle\frac{\log y}{x^{x-1}}}\right)=x\log y$

However there is a pesky $$x$$ on the RHS which won't go away. I am wondering if the people of Brilliant.org have any idea on this?

If any body is curious, $$x^x=y$$ can be rearranged as $$x=\frac{\log y}{W(\log y)}$$.

Note by Ali Caglayan
3 years ago