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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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Just confirming, because some people mean different things by $\log(x)$: Is this base-10 log, or the natural log? – apnorton Aug 25 '13 at 18:00
It doesn't really matter - I know how to convert logarithm base. But I meant natural logarithm. – gogowitczak Aug 25 '13 at 18:01
up vote 5 down vote accepted

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

follows after using the fact that

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

and a change-of-base.

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