In one place I'm reading the performance of a heapsort is
N log₂(N)
and in another it says
N log N
Are they the same?
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3Usually in computer science $\log$ denotes the logarithm in base 2. – Crostul May 14 '17 at 21:46
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Since $\log_2(N) = \frac{ \log{N}}{\log{2}}$ for all $N$, and $\log{2}$ is only a constant, they are the same in the sense that $N \log_2{N} = O(N \log{N})$, and vice versa.
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Be aware that the other side of this is not true: $O(2^N)$, $O(e^N)$ and $O(10^N)$ do not mean the same things as each other – Henry May 17 '17 at 14:01