equivalency of some facts in $O$ notation

I misunderstanding about some logarithm property in algorithm course:

is it correct that we say following three term is equivalent?

$$O(\log a + \log b)$$

$$O(\log (ab))$$

$$O(\log (a+b))$$

• $\log(a)+\log(b)=\log(ab)$ is an elementary property of the logarithms. May 4 at 15:54

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 $$b>a$$.

• You may want to add the case when a = b. May 4 at 23:45
• @MaryamPanahi: what do you mean ? May 5 at 11:32
• @MaryamPanahi: did you read the first sentence ? May 5 at 12:35