Domain of definition of $\log \log z$ Find the region where the complex function $\log \log z$ is defined.

I don't understand the question. Should I literally just find where the function is defined, or where the map $z \mapsto \log \log z$ is single-valued?
$log logz$ can be defined everywhere in the complex plane except at $z=0$ and $z=1$.
I am assuming the question asks for the points at which the function can exist.
$log logz$ can be defined everywhere in the complex plane except at $z=0$ and $z=1$.
I am assuming the question asks for the points at which the function can exist.