Function order of Logarithms

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How can I use Stirling's approximation to trying to find the function order of $ceil(log(logx))!$ ? My main goal is to finding it's order of complexity but my main issue is that I'm not sure on how to deal with this problem. I know that n! = n*(n-1)(n-2)(n-3)....3*2*1 but algorithms make it harder for me to comprehend what exactly is going on.