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[Solved]: asymptotic growth of n^log log n

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Problem Detail: 

I'm ordering functions by their asymptotic growth for an assignment and I have verified I have the correct order by using limits, but I'm trying to understand why $n^{log\ log\ n}$ is between $n^3$ and $2^n$. It seems like it should be closer to the order of $n^n$. Can anyone provide some insight on this.

Asked By : realgenob

Answered By : Yuval Filmus

It could help if you wrote $n^{\log\log n}$ as $2^{\log n\log\log n}$. Then it should be clear that $2^{\log n\log\log n} = o(2^n)$. The morale of this is that the base of an exponent doesn't count as much as the exponent itself.

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