Solve the recurrence relation T(n)=3T(√n)+lg(n)

Question

Master's Theorem is known to me, but I can't understand how to apply this theorem to this problem. So, how I will find Θ of T(n)?

Answer 1

Define $X(n) = T (2^n)$.

Then $X(n) = T (2^n) = 3T(2^{n/2}) + n = 3X(n/2) + n$.

You solve the recurrence for $X(n)$, and $T(m) = X (\log m)$.