34
$\begingroup$

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.

$\endgroup$
3
  • $\begingroup$ 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. $\endgroup$
    – Brandin
    Jun 6, 2019 at 7:45
  • $\begingroup$ "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'. $\endgroup$
    – Brandin
    Jun 6, 2019 at 7:56
  • $\begingroup$ Now what about $\lceil \operatorname{lg} x \rceil$ for computer scientists :) $\endgroup$
    – SOFe
    May 13, 2021 at 5:42

19 Answers 19

Reset to default
22
$\begingroup$

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".

$\endgroup$
21
$\begingroup$

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

$\endgroup$
6
  • 8
    $\begingroup$ 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. $\endgroup$
    – Cat
    Jun 27, 2017 at 22:11
  • 1
    $\begingroup$ South Ontario, also say "lawn". $\endgroup$
    – undergroundmonorail
    Jun 27, 2017 at 23:20
  • 2
    $\begingroup$ @Eric, yes, provided of course that we pronounce "lawn" the same way ;) $\endgroup$
    – Duncan Ramage
    Jun 28, 2017 at 18:28
  • 1
    $\begingroup$ Of course you would do that, as a member of the Canadian race! $\endgroup$
    – richard1941
    Jul 4, 2017 at 19:10
  • 1
    $\begingroup$ I have a possibly-Vietnamese student who also pronounces it 'lawn'. $\endgroup$
    – LSpice
    Dec 5, 2017 at 22:51
20
$\begingroup$

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.

$\endgroup$
1
  • 1
    $\begingroup$ 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) $\endgroup$
    – richard1941
    Jul 4, 2017 at 19:15
14
$\begingroup$

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}

$\endgroup$
17
  • 1
    $\begingroup$ 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. $\endgroup$
    – zrbecker
    Jun 27, 2017 at 19:07
  • 2
    $\begingroup$ Indeed, I would allow the meaning of $\text{“}{\log}\text{''}$ with no base to depend on the context. $\endgroup$
    – Michael Hardy
    Jun 27, 2017 at 19:09
  • 6
    $\begingroup$ 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). $\endgroup$
    – Ruslan
    Jun 27, 2017 at 19:32
  • 7
    $\begingroup$ This is overly analysis-specific. In computer science, $\log$ means $\log_2$, and specifically in big-O, $\log$ is just $\log$, no base required. $\endgroup$
    – Kevin
    Jun 27, 2017 at 21:55
  • 4
    $\begingroup$ 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. $\endgroup$
    – Luca Citi
    Jun 28, 2017 at 1:01
9
$\begingroup$

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).

$\endgroup$
6
$\begingroup$

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!)

$\endgroup$
4
  • $\begingroup$ The younger brother of a high school friend was getting his Economics Ph.D. here, when we talked about his thesis he said "lonn." $\endgroup$
    – Will Jagy
    Jun 27, 2017 at 22:29
  • $\begingroup$ Now that I think of it, Stuart did not go to the same high school as I and his brother Doug, he went to a private high school somewhere. Maybe that explains it. $\endgroup$
    – Will Jagy
    Jun 27, 2017 at 22:34
  • $\begingroup$ Do you mean lunn to rhyme with bun, or with a schwa (/ə/), to rhyme with detention? $\endgroup$
    – PJTraill
    Jun 28, 2017 at 22:05
  • 2
    $\begingroup$ I think it was to rhyme with "detention". $\endgroup$
    – Especially Lime
    Jun 28, 2017 at 22:19
6
$\begingroup$

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.

$\endgroup$
5
$\begingroup$

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.

$\endgroup$
3
  • 1
    $\begingroup$ What region on the world are you in? $\endgroup$
    – mweiss
    Jun 27, 2017 at 19:04
  • $\begingroup$ I'm from NE US and I say "ell enn" $\endgroup$
    – Rocket Man
    Jun 27, 2017 at 19:06
  • $\begingroup$ @AJStas Yes, I am also from NE US. I hear that said a lot, but as I often work math problems that use $n$ as a variable, I don't use "ell-enn" as often as "log" or "natural log". $\endgroup$
    – Franklin Pezzuti Dyer
    Jun 27, 2017 at 19:13
5
$\begingroup$

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" = $ln(x)$

$\endgroup$
5
$\begingroup$

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.

$\endgroup$
4
$\begingroup$

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

$\endgroup$
4
$\begingroup$

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

$\endgroup$
4
  • 1
    $\begingroup$ 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." $\endgroup$
    – user49640
    Jun 27, 2017 at 20:34
  • $\begingroup$ @user49640 I live in the USA though and she teaches in English. $\endgroup$
    – Ovi
    Jun 27, 2017 at 20:35
  • 1
    $\begingroup$ I think it's safe to say that this is a mistake on her part due to insufficient knowledge of English. $\endgroup$
    – user49640
    Jun 27, 2017 at 20:36
  • 1
    $\begingroup$ @user49640 I agree, it's probably closer to how they pronounce it in her country; nevertheless, I thought this pronounciacion might be interesting still. $\endgroup$
    – Ovi
    Jun 27, 2017 at 20:40
4
$\begingroup$

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.

$\endgroup$
4
$\begingroup$

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).

$\endgroup$
1
  • $\begingroup$ I made the same comment, but it seems to have been deleted by the moderators for some reason. $\endgroup$
    – user49640
    Jun 28, 2017 at 11:01
4
$\begingroup$

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.

$\endgroup$
1
  • 1
    $\begingroup$ Ambiguity is a sin, or ambiguity is a log? :-) $\endgroup$
    – LSpice
    Dec 5, 2017 at 22:54
3
$\begingroup$

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.

$\endgroup$
2
$\begingroup$

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

$\endgroup$
1
  • $\begingroup$ @RDK Please look at all the other answers. Some are about as long as this one yet they have received many votes $\endgroup$
    – Kamal Saleh
    Feb 10 at 17:31
1
$\begingroup$

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.

$\endgroup$
0
0
$\begingroup$

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.

$\endgroup$
1
  • $\begingroup$ natural log (base $e$). $\endgroup$
    – amWhy
    Oct 20 at 18:26

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .