# Is it correct to use 'Ln' instead of 'ln' for natural logarithm?

In some research papers, authors use 'Ln' for natural logarithm instead of 'ln'. Is it correct?

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Research papers in Statistics or allied disciplines? – Scortchi Jan 28 '14 at 21:18
A rose by any other name would smell as sweet. I would say it is fine as long as it is clear what is intended. – Marc Claesen Jan 28 '14 at 21:19
In others, they use "log" and they mean the natural logarithm. – Alecos Papadopoulos Jan 28 '14 at 21:21
I'd say 'ln' is standard & anything that makes the reader doubt the sense of what's written even momentarily is a bad idea. And that standards vary by discipline, which is why I asked about that. – Scortchi Jan 28 '14 at 21:24
The only serious problem I see is the fact that Ln is already a "thing" in mathematics (I regard Mathematica's use of capitals on functions as something of a problem for that reason). If there's no danger of confusion it might be okay, but when in doubt, especially when using nonstandard notation, always explicitly define it. – Glen_b Jan 29 '14 at 0:19

Why wouldn't it be? As long as it isn't confusing.

However, it is sometimes the case (especially when writing in non-mathematical fields) that there is confusion over base 10 vs. base e, and often people in those fields haven't heard of (or have forgotten about) the difference between ln (or Ln) and log.

If there is possibility of confusion, it is best to specify the base, and do so explicitly: $\log_{10}$ or $\log_\mathrm{e}$ or $\ln$ (base e logarithm) or something similar.

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I am writing a paper and I want to calculate log (with base e) of my data set. then, if I use 'Ln' or 'ln', there is not any difference? which one is better to use in a paper? – PSS Jan 28 '14 at 21:29
I think 'ln' is far more common than Ln, at least in the fields I am familiar with. If you are in physics then doubtless your readers are familiar with different logarithms. If in psychology, well.... I wouldn't assume it and might add a footnote. – Peter Flom Jan 28 '14 at 21:32
It's been "ln" for just about 100 years. Can you think of one good reason for writing "Ln" instead? In any paper I was reviewing or editing I would always recommend "ln". What next, "Exp", "SIN"? – Nick Cox Jan 28 '14 at 21:37
@nik: There shouldn't be, but I can attest there sometimes is. Stating the base explicitly is sound advice when your readers may not be very mathematically savvy. – Scortchi Jan 29 '14 at 9:11
There is possible confusion and I have seen it. When your last exposure to "common" vs. "natural" log was years ago, it's easy to forget. I have seen this with both PhDs and MDs. – Peter Flom Jan 29 '14 at 11:33

Be careful, because the notation $\mathrm{Ln}$ is currently used in mathematics. For $z\in\mathbb{C}$, the complex logarithm is the multivalued function defined by $$\mathrm{Ln}(z) = \ln(|z|)+i(\arg(z)+2k\pi)$$ for $k=0,\pm 1,\pm 2, \dots$. Hence, you should check the mentioned papers to verify in which context they use the $\mathrm{Ln}$ notation.

Also, there is some multiplicity of notations. For instance, some people write $\ln(z)$ for the complex logarithm of $z$ and use $\mathrm{Ln}(z)$ to denote its principal value (the value with $k=0$). The notations $\mathrm{Log}(z)$ and $\log(z)$ are also commonly used with the same mixed meanings.

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+1. Excellent point, and embarrassed recognition from (one of) those who had forgotten this because they never use it in their statistical work. I'd still wager that most occurrences of "Ln" in statistical contexts are typos for "ln". – Nick Cox Jan 29 '14 at 0:14
I believe you're right, Nick. Probably just typos. – Zen Jan 29 '14 at 0:18

The forms $\ln$ or $\log_\mathrm{e}$ are standard in all fields I'm familiar with. Though $\mathrm{Ln}$ might've become a standard, it didn't; & though it's unlikely to cause more than a momentary hesitation on the reader's part, even that is worth taking pains to avert. Moreover, I've noticed that its use is correlated with the commission of graver mathematical solecisms, so you may want to eschew it to avoid making a bad impression among those that know and care about such things.

In business notation is often sloppy, & while you're likely to see $\mathrm{Ln}$ often enough, it doesn't constitute an alternative standard, or necessarily result from a deliberate choice—could well be due to Powerpoint's autocorrect feature.

† Complex analysis isn't one of them—see @Zen's answer.

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That's a good point - using non-orthodox notation can signal that you don't know what you are doing (even if you do). – Peter Flom Jan 28 '14 at 21:53
@Peter: Yes, the effect of accumulated irritation at each double-take plus the nagging doubt whether the author really knows what he's talking about can be that you toss away the paper half-read. Unfair perhaps to rely on such heuristics, but life is short. – Scortchi Jan 28 '14 at 22:32

My guess is they were worried that in whatever typeface the paper was published in, the ln would look too much like the word In. I saw a typescript (dating myself) where ℓn [that is Latex \ell] was used, which meant changing the type ball of an IBM Selectric.

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Good point, though a much better solution would have been to change the typeface. It's only a problem with sans serif fonts & I can't see any reason to insist on using those for mathematical expressions. Some people want to: it's come up here. – Scortchi Jan 29 '14 at 10:36
An author has little choice about the typeface a journal is published in. Many probably won't even know. – Peter Flom Jan 29 '14 at 11:34
@Peter: Good point too - it could be a precaution. But I was thinking of conference papers, as per the OP's comment, which aren't always typeset & published by the organizers. I'm pretty sure there's no journal that would put mathematical expressions into sans serif. – Scortchi Jan 29 '14 at 13:21