How would i go about calculating the Big Theta of the following nested loop?
Each internal loop does $2^i$ iterations of $\Theta(1)$ so it takes $\Theta(2^i)$.
Therefore the time complexity of the code is the $\Theta(\Sigma_{i=0}^{log(n)} 2^i)=\Theta(n)$.

You could intuitively think of summation here as writing in binary base a number where all its digits are 1, and has the same number of digits as n, it is linear to the size of n.