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This is correct, but in case it makes more sense this way (it does to me):

log (base X) Y === log (base e) Y / log (base e) X

So the difference between log (base 2) and log (base 10) is just the difference between being divided by log (base e) 2 or log (base e) 10. Since those are both constant factors, big-O notation doesn’t care.

It's actually the same statement after all just with and without the actual math. But yes, it's very easy to see it from this.

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