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This question already has an answer here:

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)?

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marked as duplicate by David Richerby, Apass.Jack, Evil, Yuval Filmus algorithms Feb 7 at 5:00

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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 $T(m) = X (\log m)$.

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