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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
2 years, 6 months ago

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