How to compare the growth rate between $lnln n$ and $2^{lg^* n}$

Mathematics Asked by Aesop 의섭 on November 30, 2020

Simple question, I’ve read in the answer sheet that the growth rate of $lnln n$ is bigger than $2^{lg^* n}$, but I can’t figure out how to prove it. Could someone help me out pls?

P.S. lg* is the iterative logarithm often used in algorithmic analysis.

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