we learned that the running time, T (u), of the successor query satises: T (u) = 3T (u) + O(1) Use this to analyze the running time of successor query.

From the note i found that the answer should be theta(lgu)^lg3) but some other note show that the right answer should be O(lg lg u) or O(log log u)

i donot know which one is the right answer, and please show me the step of proof( recursion tree or master therome)