TITLE: Using $\ln$ or $\log$
QUESTION [7 upvotes]: In my paper, I have $\ln$, $\log$ and $\log_2$. But, I have used both $\ln$ and $\log$ interchangeably. I wanted to be consistent and use just one of them. Which one is better?
1) I choose $\ln$, then I have to use it when stating the results in terms of Big O, e.g., $O(n \ln{n})$. Is that OK? I have seen that when people state order-results, they use $\log$ in Big O. 
2) I choose $\log$, and the first time I use it, I mention that the base of the logarithm in this paper is by default $e$.
Which one is better? If I want to use the second solution, what is the best way to state that?

REPLY [2 votes]: I suggest you use $\ln$ in the paper and $\log$ when you have order results (since the base of $\log$ does not matter, but it is conventional to use $\log$ when stating order results).