I misunderstanding about some logarithm property in algorithm course:
is it correct that we say following three term is equivalent?
$O(\log a + \log b)$
$O(\log (ab))$
$O(\log (a+b))$
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asked May 4, 2022 at 13:04
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1$\begingroup$ $\log(a)+\log(b)=\log(ab)$ is an elementary property of the logarithms. $\endgroup$– user16034May 4, 2022 at 15:54
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1 Answer
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Let $a>b>0$. From $\log(a+b)=\log(a)+\log\left(1+\dfrac ba\right)$, we draw
$$\log(a)\le\log(a+b)\le \log(a)+\log(2)$$ and similarly for $b>a$.
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$\begingroup$ @MaryamPanahi: what do you mean ? $\endgroup$– user16034May 5, 2022 at 11:32
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$\begingroup$ @MaryamPanahi: did you read the first sentence ? $\endgroup$– user16034May 5, 2022 at 12:35