[Solved]: Are $\log_{10}(x)$ and $\log_2(x)$ in the same big-O class of functions?

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Are $\log_{10}(x)$ and $\log_{2}(x)$ in the same big-O class of functions? In other words, can one say that $\log_{10}(x)=O(\log x)$ and $\log_{2}(x)=O(\log x)$?

Asked By : David Faux

Answered By : Dave Clarke

Yes. Because they differ only by a constant factor. Remember high school math:

$\log_2 x = \dfrac{\log_{10} x}{\log_{10}2}$.

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Question Source : http://cs.stackexchange.com/questions/4968

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