can anyone help me with that question

Question

what is the domain of log(log(x)the base is 0.2)

Answer 1

Since the domain of log(x) is x > 0,
we need log(x) > 0
that is, 0 < x < 0.2

You can see this reflected in the graph found below. The domain is where the imaginary part is zero.

http://www.wolframalpha.com/input/?i=log_.2%28log_.2%28x%29%29

Answer 2

the question was log(log_.2(x))
the base of the first log is 10 then the base of the second log which is inside the brackets is 0.2