What is the domain of the function log(log(sinx))?

Question

If log4 + log(13x+1) = log(5x+9) + 1, then what is the value of x?

Note: Assume all log represented is to the base of 10.

Answer 1

Sin (x) : Range = [-1,1]
log (Sin (x)): Range = (-∞,0]
log (log (Sin (x))): Range = [∅] (null Set)
Therefore Domain = [∅] (null Set).