Why is the natural logarithm represented by $\ln$?

Question

The natural logarithm is often represented by several different notations:

It is the third notation that has me wondering. Why is $\ln$ used, and not, say, $\text{nl}$? My two theories about this are

Why is the notation $\ln$?

I guess this just stands for Logarithm Natural (in some languages like French, they use this order of the words). Do you really think that this is really an interesting/important question on the history of Math and Sciences? — Alexandre Eremenko, Sep 07 '15 at 18:24
@AlexandreEremenko It's about the history of notation, which is a valid subject. — HDE 226868, Sep 07 '15 at 18:25
In pure mathematics (unlike in applied computations) they use only natural logarithm. So they abbreviate it as $\log$. — Alexandre Eremenko, Sep 07 '15 at 18:26
@AlexandreEremenko Yep, I read that; $\ln$ is used mainly in physics and engineering. — HDE 226868, Sep 07 '15 at 18:26
Formally this is a valid subject. But on my opinion the question is trivial and not important. — Alexandre Eremenko, Sep 07 '15 at 18:28
In Spain and Spanish-speaking countries, ln = 'logaritmo natural', but more frequently 'logaritmo neperiano' — xxavier, Feb 11 '20 at 12:46

score 8 · Answer 1 · edited Feb 11 '20 at 00:42

8

As far as I am aware, the mathematical operator commonly spelled $\ln$ is an abbreviation of the Latin term, logarithmus nātūrālis.

I am not sure who first used this abbreviation, but I suppose it very well may have been Napier.

I remember having seen ln written as an abbreviation of two words in the form $l.n.$

edited Feb 11 '20 at 00:42

tchrist

answered Sep 09 '15 at 22:58

user80034

4

This question (of course) has been asked before. See http://math.stackexchange.com/questions/1694/how-did-the-notation-ln-for-log-base-e-become-so-pervasive, and note the answer by Velleman, which gives support to this answer. – KCd Sep 10 '15 at 01:44

Mauro ALLEGRANZA · Answer 2 · 2015-09-10T15:38:41.690

6

$\ln$ (for natural logarithm) was used in 1893 by Irving Stringham (1847-1909) in Uniplanar Algebra (Cajori vol. 2, page 107).

Thnaks to KCd's reference in his comment, we have an earlier occurrence :

edited Sep 10 '15 at 15:38

answered Sep 07 '15 at 18:47

Mauro ALLEGRANZA

I should have seen that! I was looking in a related page the other day. Any idea why Stringham chose it? – HDE 226868 Sep 07 '15 at 18:49

2 Answers2