Which is more preferable to write $\log(x)$ or $\ln(x)$ Which one is more preferable to write when you are writing an exam. Is it $\log(x)$ which denotes the natural logarithm or is it $\ln(x).$
 A: If you're in doubt, "$\ln$" will always unambiguously denote the natural logarithm.
If you prefer "$\log$", there's a wide range of situations where you can get away with writing that, such as in a course where you know the teachers use that, or when your calculations make it clear that you can only mean the natural log (e.g., if your write "$e^a=b$ and therefore $a=\log b$", there's not much room for misunderstanding). And in general in everything branded as pure math.
But if you want to play it safe, there's no relevant reason not to write "$\ln$". (Except if you happen to know the teacher who will mark the exam personally hates the "$\ln$" notation, but that would be unusual).
A: It often depends on context.  In lower level classes it tends to be written as $\ln x$ to distinguish it from $\log_{10} x$, but in higher level class such as complex analysis or analytic number theory, the natural logarithm is the only log that matters and so is not likely to be confused with $\log_{10}$. So, in these settings, $\log x$ is used. Ultimately, of course, it's simply a matter of personal preference.
A: For a pure mathematician, exp is the exponential and log is the logarithm. I tend to ``hate'' people who understand $\log = \log_{10}$, since especially when I must assess my own students.
Of course I am joking, but actually $10$ is a very unnatural base for higher mathematics. We use it because we have ten fingers, and Mickey Mouse would therefore understand $\log=\log_8$! In differential calculus it is highly preferable to have a clean formula like $D\log x = 1/x$, while for computational purposes a logarithm in base $2$ could be preferable.
A: If you're taking a physics exam, do $\ln(x)$ if youre taking a math exam do $\log(x)$. From my experience, the base $10$ logarithm is not the default in mathematics at all, it has no merit. It is however a very useful tool for us to estimate the sizes of units so physicists like it alot and would get confused if you don't write $\ln(x)$ for the natural logarithm.
(This of course depends on your educational level but if youre at university, I would suggest doing this.)
