convert log(log(x)) to x-based power

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I'd like to convert log(log(x)) to x-based power (I mean $x^{something}$). How can I do that?

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$$\log(\log(x)) = x^{\log(\log(\log(x)))/\log(x)}$$

follows after using the fact that

$$x = e^{\log x}$$

and a change-of-base.