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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 $\ln(x).$

Git Gud
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sayan chattopadhyay
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    (Personally) I prefer $ln(x)$. I leave $log(x)$ for the logarithm in base $10$. – Daniel Apr 05 '15 at 13:38
  • i really dont get which one to write – sayan chattopadhyay Apr 05 '15 at 13:39
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    One has $\log >\ln$. – Git Gud Apr 05 '15 at 13:39
  • There is no single answer to the question, other than do whatever the teacher does since the main point is simply to make sure you are properly understood. If you're not talking about an exam in a class, then see http://math.stackexchange.com/questions/1694/how-did-the-notation-ln-for-log-base-e-become-so-pervasive, http://www.reddit.com/r/math/comments/2m7ytg/when_you_see_logx_is_that_normally_implied_to_be/, http://forums.xkcd.com/viewtopic.php?f=17&t=66988 – KCd Apr 05 '15 at 13:48
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    Everyone uses $\log$ for the logarithm that is most common in their field; it's base $2$ in computer science, base $e$ in selected areas if math. But if you use $\ln$, there is absolutely no ambiguity about what's meant; why not use $\ln$? – pjs36 Apr 05 '15 at 13:49
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    By the way, in American English it is teachers than write an exam while students take an exam. (Think about books: would you say the author writes the book or the readers write the book?) Some people might misunderstand the first sentence in the question, thinking it is coming from a teacher (not that this is terribly important). – KCd Apr 05 '15 at 13:51
  • @GitGud Perhaps I am missing something, but I feel like your comment does neither answer the OPs question nor does it seem to be correct: http://i.stack.imgur.com/M9GM5.png – Phil-ZXX Apr 05 '15 at 14:46
  • It was a (half) joke, I meant that $\log$ is a superior notation. – Git Gud Apr 05 '15 at 15:49
  • I don't think the purported duplicate is one. The older question asks for historical information, this one for a practical recommendation. I have difficulty imagining an answer that would satisfy both. @Jyrki. – hmakholm left over Monica Apr 05 '15 at 16:24

4 Answers4

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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).

hmakholm left over Monica
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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.

Tim Raczkowski
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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.

Siminore
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  • Mathematicians tend to use $\log$ instead of $\ln$ because there is only one logarithm (that mathematicians care about). There is nothing special to base ten. By writing $\log$, you are, in a way trying to say, the most important logarithm, as you drop the base. The use of $\ln$ mainly appears in basic undergraduate courses. – Nicolas Bourbaki Apr 06 '15 at 04:34
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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.)

Lundborg
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