Base of logarithm in runtime of Prim's and Kruskal's algorithms For Prim's and Kruskal's Algorithm there are many implementations which will give different running times. However suppose our implementation of Prim's algorithm has runtime $O(|E| + |V|\cdot \log(|V|))$ and Kruskals's algorithm has runtime $O(|E|\cdot \log(|V|))$.

What is the base of the $\log$?
To expand on what David Eppstein said, you can assume it's in any base.

If the log were initially in base $b$, it is asymptotically the same as if it were in base $k$:  

$$O(\log_b n) = O\left(\frac{\log_k n}{\log_k b}\right) = O(\log_k n)$$

because $k$ and $b$ are both constants; $\log_k b = O(1)$.

The logs in any two bases are the same in big-O notation.