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

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.