Show that $Log( Log z$) is analytic in the domain consisting of the $z$ plane with a branch cut along the line $y = 0, x ≤ 1$.
As of now im not too sure on how to solve this problem, so i was thinking you may have to use the Cauchy-Riemann equations to find the answer. I honestly tried it but I don't know what to do.
If someone can help me out in solving this problem that would be great. Thanks!