The total time complexity is Θ(n). To see this, note that the inner loop does Θ(i) work per iteration, and that i takes on the values 1, 2, 4, 8, 16, 32, ..., 2log n. If we sum this up, using the formula for the sum of a geometric series, we get
1 + 2 + 4 + 8 + ... + 2log n = 2log n + 1 - 1 = 2 · 2log n - 1 = 2n - 1
So the total work done is Θ(n).
Hope this helps!