34

I have always heard an expression like $\ln (x^2)$ pronounced aloud as "ell-enn ex squared". That is, the name of the function $\ln$ is read aloud as a two-letter abbreviation. However, I recently came across a Youtube video in which the speaker consistently pronounces $\ln$ as if it were a single syllable, something like "linn" or "lunn". So $\ln (x^2)$ would be spoken aloud as "linn ex squared".

The speaker in that video has what sounds to me like an Australian accent (apologies to any Kiwis if he is actually a New Zealander) so I am wondering if this is something that varies from country to country — I am from the United States and have never heard it pronounced that way.

So the question: How do you pronounce $\ln$? How is it pronounced by others in your locale?

Please include in your answer any important regional information (Edit: or professional context) that might be significant.

EDITED TO ADD: I am fully aware that many mathematicians prefer to use the notation "$\log x$" for $\log_e x$, and many object to the use of $\log$ for $\log_{10}$, AKA the "common logarithm". Please do not use this question as an opportunity to argue whether $\log_e$ or $\log_{10}$ is more "natural". For the purposes of this question, assume that you are in a context in which the notation $\log$ is reserved for $\log_{10}$, and $\log_e$ is denoted by $\ln$. The question is not about whether or not that notational convention is a good one, it is about how to pronounce it.

SECOND EDIT: I should have thought to include this in my original post, but it may be that the pronunciation varies according to professional context as well: that is, perhaps the mathematicians at your university pronounce it "log", the chemists pronounce it "ell en", and the high school teacher down the block says "lunn". So when answering the question, please provide any relevant context details that might help clarify the scope of your response.

mweiss
  • 24,547
  • I have seen some textbooks that propose "lawn" as a pronunciation for this symbol, but in practice I have never heard a math teacher prefer that pronunciation (I am from the U.S.) when discussing an expression involving this symbol. Probably "ell en" will be used by default because it is not that hard to say (it is only two syllables as opposed to the single syllable 'lawn'). As a shorthand I suspect 'linn' is probably easier to say than 'lawn', so if you wanted a very lazy way to say it, 'linn' would probably be easier. – Brandin Jun 06 '19 at 07:45
  • "it may be that the pronunciation varies according to professional context" - Yes. If you teach someone about ln (natural log) for the first time, I suspect you will naturally say the longer "natural log" for this symbol for clarity until your audience gets used to it. Once you use something over and over, however, you will naturally try to find an easier way to express such a thing. For me a/b is "a over b" even if you don't actually write 'a' literally 'over top of' b, as is done in a fraction, because division is so common, and saying 'over' is much easier than saying 'divided by'. – Brandin Jun 06 '19 at 07:56
  • Now what about $\lceil \operatorname{lg} x \rceil$ for computer scientists :) – SOFe May 13 '21 at 05:42

19 Answers19

22

Vancouver, Canada. I exclusively pronounce it as /lɑn/.

Duncan Ramage
  • 7,103
  • 8
    Just to verify for us IPA noobs: This would be the same as the pronunciation of lawn, correct? (Based on this.) If so, can confirm that Calgary, Canada also pronounces it that way. – Cat Jun 27 '17 at 22:11
  • 1
    South Ontario, also say "lawn". – undergroundmonorail Jun 27 '17 at 23:20
  • 2
    @Eric, yes, provided of course that we pronounce "lawn" the same way ;) – Duncan Ramage Jun 28 '17 at 18:28
  • 1
    Of course you would do that, as a member of the Canadian race! – richard1941 Jul 04 '17 at 19:10
  • 1
    I have a possibly-Vietnamese student who also pronounces it 'lawn'. – LSpice Dec 05 '17 at 22:51
  • My high school calculus teacher pronounced it this way (in the 1990s, in the United States). And then I never heard anyone pronounce it this way again. So it's interesting to see that others pronounce the natural logarithm function this way as well. (I had no idea... I assumed that my teacher just made it up.) – Richard Sullivan Sep 01 '21 at 01:00
22

I live in the US, so I pronounce Ln as "ell enn" or I sometimes say natural log.

If I had the expression ln($x^2$) I would say: "ell enn of ex squared".

BBot
  • 917
20

As a non-native English speaker who has to read mathematical expressions quite frequently, I use the following guides:

  1. Handbook for Spoken Mathematics, Research and Development Institute, Inc: This is probably the most complete reference. Not of easy consultation, though.
  2. H. Valiaho, Pronunciation of mathematical expressions (pdf): A short list divided by topic (e.g. Logic, Sets, Functions etc.). Reports also variants.

For what concerns $\ln$, these guides recommend:

the natural log of x

from [1] and [2];

l n of x

from [1], and this coincides with your example; [2] recommends other pronunciations too, but I suspect they are rarer.

Massimo Ortolano
  • 744
  • 1
    Thank you for the first real answer that goes beyond, "we do it this way over here". Even in the U.S., Boston, New York, Virginia, California, and Texas have different pronunciations, of which only California is correct, of course. (in English, not in Spanish) – richard1941 Jul 04 '17 at 19:15
14

I would pronounce $\ln x$ as "log ex", and usually write it as $\log x,$ or sometimes when speaking to freshmen or similarly inexperienced people, as $\log_e x$ .

It is unfortunate that secondary-school algebra textbooks teach students that "log" with no subscript always means the base-$10$ logarithm. Since the natural logarithm is indeed the natural logarithm to use in calculus, it is written as $\log$ with no subscript. Some mathematicians write it as $\ln$ but still understand $\log$ written by others to mean the base-$e$ logarithm. Only among non-mathematicians is that last fact unknown.

What is "natural" about it can be seen here: \begin{align} & \frac d {dx} \log_{10} x = \frac{\text{some consant}} x \\[10pt] & \frac d {dx} \log_6 x = \frac{\text{some other constant}} x \\[10pt] & \text{etc. But only when the base is $e$ rather than 6 or 10 or some} \\ & \phantom{\text{etc. }} \text{other number besides $e$ is the “constant'' equal to 1, i.e.} \\[10pt] & \frac d {dx} \log_e x = \frac 1 x. \end{align}

Michael Hardy
  • 1
  • 1
    You successfully argued that in calculus base-$e$ is a natural base, but from a secondary-school algebra point of view does your argument hold water? I prefer the notion that $\log x$'s base is contextual, and we explicitly write the base or use another name when the base is not clear from context. – zrbecker Jun 27 '17 at 19:07
  • 2
    Indeed, I would allow the meaning of $\text{“}{\log}\text{''}$ with no base to depend on the context. – Michael Hardy Jun 27 '17 at 19:09
  • @zrbecker I don't think we had all that much chance to use ln at all in my high school algebra class. In precalculus we were saying "natural log", and by a few weeks into calculus it was just "log" :) – hobbs Jun 27 '17 at 19:23
  • 6
    Only among non-mathematicians is that last fact unknown. Actually also among non-native-English people in some places. When I first saw $\log x$ I first thought something was missing there due to a typo, and only after some research I found out that it wasn't a typo and was meant to be $\ln x$ (which is the only common way we write $\log_e x$ in Russia). – Ruslan Jun 27 '17 at 19:32
  • 7
    This is overly analysis-specific. In computer science, $\log$ means $\log_2$, and specifically in big-O, $\log$ is just $\log$, no base required. – Kevin Jun 27 '17 at 21:55
  • 1
    @Kevin : As I said, I think it should depend on context; I never said $\log$ should always mean $\log_e.$ I have seen $\lg$ used for $\log_2. \qquad$ – Michael Hardy Jun 27 '17 at 22:53
  • @Ruslan I remember being very surprised that in Russia the $\ln$ notation is used by mathematicians, including for the $p$-adic logarithm where there is no base at all. – KCd Jun 28 '17 at 00:43
  • 4
    According to the ISO 80000-2 standard, the natural logarithm $\log_e $ should be written $\ln $ and not $\log $, which is only allowed when the base is irrelevant. – Luca Citi Jun 28 '17 at 01:01
  • 1
    So much for ISO. $\qquad$ – Michael Hardy Jun 28 '17 at 03:14
  • 1
    The ISO standard is for mathematical notation used in the physical sciences, not in mathematics. – user49640 Jun 28 '17 at 15:26
  • How does the fact that the constant obtained on differentiating the function, is equal to 1 instead of 2.303 or any other such number make $\log_e$ any more (or less) "natural" than others? – HeWhoMustBeNamed Nov 01 '17 at 17:55
  • @Michael Hardy, thanks corrected. Now can you reply to my doubt? – HeWhoMustBeNamed Nov 01 '17 at 18:06
  • @MrReality : If you find the base that makes the constant equal to $1,$ then the problem of differentiating logarithm functions with other bases is reduced to that case, thus: $$ \frac d{dx}, \log_2 x = \frac d{dx}, \frac{\log_e x}{\log_e 2} = \frac d{dx}, \frac{\log_e x}{\text{constant}} = \frac{1/x}{\text{constant}} = \frac{1/x}{\log_e 2}. $$ It's the same as the reason why radians are natural: $$ \frac d {dx}, \sin x = \big( \text{constant} \cdot \cos x\big). $$ Only when radians are used is the "constant" equal to $1. \qquad$ – Michael Hardy Nov 01 '17 at 18:14
  • @MrReality : And likewise with exponential functions: $$ \frac d{dx}, a^x = \big( \text{constant} \cdot a^x\big). $$ If you know the particular base in which the "constant" is $1,$, then you reduce the other cases to that case, thus: $$ \frac d{dx} 2^x = \frac d{dx} e^{x\log_e 2} = \cdots $$ and use the chain rule and then simplify and get $$ \frac d {dx} 2^x = 2^x\cdot\log_e 2. $$ – Michael Hardy Nov 01 '17 at 18:20
  • @MichaelHardy, So is it the actual reason why it ( i.e, $\log_e$) is called "natural" log, I mean is it all there is to it?
    And regarding the second part of your comment I'm a slightly confused$:$ isn't the derivative of $\sin x$ when, say, $ x=90^{\circ}$ equal to zero? (Just like when $x=\frac\pi2 $)?     – HeWhoMustBeNamed Nov 01 '17 at 18:28
  • @MrReality : I don't know why anything I wrote would be construed as meaning the derivative of the sine function evaluated at a right angle is anything other than zero. One has $$ \frac d {dx} \big( \text{sine of $x$ degrees} \big) = \left( \frac \pi {180} \times \text{cosine of $x$ degrees} \right) $$ and therefore at $90^\circ$ the derivative is $0.$ But the constant factor is $\pi/180,$ whereas when radians are used, it is $1{:}$ $$ \frac d {dx} \big( \text{sine of $x$ radians} \big) = \big( 1\times \text{cosine of $x$ radians} \big) . $$ – Michael Hardy Nov 01 '17 at 21:42
  • For computer scientists, neither $e$ nor $10$ is natural. Base $2$ is the only natural base. Fortunately we use $\operatorname{lg} x$ instead of creating the third standard :) – SOFe May 13 '21 at 05:43
9

In general practice I say "log," no matter what, and if a specific base is used I say "base-n log." Special cases include "binary log" for a base-2 log, which I write $\lg$.

For $\ln$ I just say the letters "ell-enn" or rather just the whole darn thing - "natural log." I sometimes have heard put emphasis on the L and say "lin" or "len," but it's rare that I do.

I'm speaking as a US student - I live in Texas but am not really native to any other state (though I did live in San Diego for high school).

Sean Roberson
  • 10,119
6

When I was at school (in England), we pronounced it "lonn", but I am sitting next to an (English) maths teacher, who says "lunn". I now just pronounce it "log" FWIW.

(To clarify, I pronounce it "log ex" even in contexts which require me to write $\ln x$, which I sometimes have to deal with!)

Especially Lime
  • 46,692
6

I am an Israeli studying at a very international Australian university.

In Israel we say "lan" (pronounced close to the English word "gun"). Here I was exposed to so many variations:

  • Saying the two letters l n
  • Saying "log"/"logarithm"
  • Saying "natural log"
  • Saying "log e"

All of the above were native-English speakers from different parts of the world. No one pronounced it like we Israelis do, as "lan".

As for your "linn", I believe it was a New Zealander. Their e's sound like i's sometimes.

Gimelist
  • 563
5

When spoken aloud, the only way that I have ever said it or heard it being said is as "the natural log of $x$ squared" or "log of $x$ squared". I have also sometimes head it said "ell-enn", which is a big time saver, but can be the wrong way to go if you are also dealing with other variables.

I have never heard somebody use "linn" or "lunn" before, though it does also seem like a good way to save time while speaking without confusing it with the names of variables.

Franklin Pezzuti Dyer
  • 40,930
  • 9
  • 80
  • 174
5

Going to high school in Texas, I always said it as an abbreviation: "el en of ex." Then when I took AP Stats, my Stats teacher was from Canada and she said "lawn of ex." I actually picked up that habit to distinguish the two:

"log of ex" = $log(x)$

"lawn of ex" = $ln(x)$

ruferd
  • 564
5

I once pronounced it "lin" in front a bunch of math geeks and they all laughed at me. (I'm in the US.) I had actually never heard it pronounced before and they all had a bunch of times.

I've also heard "log-en" for the natural log, but usually just "log" if you're not being specific.

Joel M Ward
  • 151
4

I am used to:

  • The natural logarithm of ( )
  • lin ( )
  • log ( )

Remember $$ \ln(x) =\log_{2.718...}(x) $$ so it is justifiable to refer to it as log

DWD
  • 635
4

My proessor is from Central/Eastern Europe and she pronounces $\ln x$ as "Logaritmus x".

Ovi
  • 24,817
  • 1
    I'm not certain, but I have the impression that the OP was asking about English. Even if that isn't the case, my impression is that many languages are spoken in "Central/Eastern Europe." – user49640 Jun 27 '17 at 20:34
  • @user49640 I live in the USA though and she teaches in English. – Ovi Jun 27 '17 at 20:35
  • 1
    I think it's safe to say that this is a mistake on her part due to insufficient knowledge of English. – user49640 Jun 27 '17 at 20:36
  • 1
    @user49640 I agree, it's probably closer to how they pronounce it in her country; nevertheless, I thought this pronounciacion might be interesting still. – Ovi Jun 27 '17 at 20:40
4

This topic was the cause of many fairly heated arguments when I was a 16/17-year-old student. In the UK at least, "ell-enn" and "lun" are quite common. In university, "log" was all that mattered. It's like how a/b is both "a upon b", "a over b" and "a divided by b": once you get to a certain level, everyone knows what you mean and you don't feel the need to argue about it.

Landak
  • 143
4

I'm Australian and his accent sounds British to me rather then aussie. I can only remember having heard it pronounced as el en or log in Australia, from this reddit post, where I can see two responses talking about pronouncing it lun, both of which are UK (one says he heard that pronunciation doing his A-levels, the other says it explicitly).

N A McMahon
  • 341
4

Since I deal mostly with logic on a daily basis, ambiguity is a sin. I always say "natural log", or "log base e" to prevent misinterpretation due to the ambiguity of just saying log.

3

From an American computer science background (we use logs too!), we typically just call it "log" regardless of whether it's a natural log or not. In applications where the log being a ln actually matters we just say "natural log". I've heard "l n" as well (el en), but it seems less common. I've also heard "lin" but it's rare enough that it sounds weird when I hear it.

rococo
  • 133
2

From China(mainland).
As I know, all schools and universities around China use a pronunciation similar to "law in"(or /ˈlɑːɪn/) to refer to $\ln$.

Oren Zhong
  • 21
  • @RDK Please look at all the other answers. Some are about as long as this one yet they have received many votes – Kamal Saleh Feb 10 '23 at 17:31
1

To my experience, at least within the field of mathematics, most people call it "log" simply.

It is safe to say that when talking of mathematics, it is universal accepted that ln is natural. Thus when mathematicians say log, they most likely refer to ln, not $\log_{10}$. Your situation that "log" means exclusively $\log_{10}$ (which you worry) shall be rare. If someone ever uses $\log_{10}$, he or she probably adds, "I mean the common log, with base 10."

Laypeople (I suppose) seldom use log (in each sense), so I am not worried about confusion.

Violapterin
  • 1,745
0

So I learned math first in the US but I am currently going to university in Canada. In the US it is always "ell-en", but in Canada, I've heard a few variations:

My physics prof says "lawn", some people I know from Nova Scotia say "lawn" or "Lan" (A in the US pronunciation of can or bat), my friend from Saskatchewan says "ell-en", and my math prof bounces around all three of those.

Josh
  • 1