Talk:Natural logarithm

Section on origin of the term

I've just removed the section titled Origin of the term natural logarithm. There was a ton of WP:OR/WP:SYNTH in here. The one source listed (which I had to check an archived copy of) didn't seem to actually verify anything at all in here. At best, it was just some extra history capped off with a statement to the effect of: "and that's why it's called the natural logarithm". If anyone disagrees or thinks any of this could/should be salvaged, please feel free to comment. –Deacon Vorbis (carbon • videos) 13:45, 18 July 2019 (UTC)

• Good call. —Kusma (t·c) 17:50, 18 July 2019 (UTC)

Read above section "Why natural"? Also see History of logarithms and recall previous name Hyperbolic logarithm. Justification for removal is weak. — Rgdboer (talk) 21:46, 19 July 2019 (UTC)

I'm not sure why concerns about OR/SYNTH are weak, and reading the above section really only strengthens my concerns there. This looks like a reading of primary source material and making conjectures based on that (however plausible doesn't matter). If someone can find a good history source that can confirm any of this, then great, but otherwise, I don't really understand the resistance here. –Deacon Vorbis (carbon • videos) 22:16, 19 July 2019 (UTC)

In science the term natural philosophy is associated with perceptible phenomena. In mathematics it is area which forms the perceptible quantification of natural logarithm. Would you please consider the quotation from Tom Whiteside on History of logarithms. Your challenge of this origin of the descriptor natural perpetuates ignorance of the concept and its relation to hyperbolic angle. — Rgdboer (talk) 21:48, 20 July 2019 (UTC)

After reading this I am actually less convinced that "naturalness" of the log is related to hyperbolic area. —Kusma (t·c) 15:25, 21 July 2019 (UTC)

(Whoops, forgot to reply.) I don't understand; are you claiming that the use of "natural" in "natural logarithm" is related to its use in "natural philosophy" (which itself is really just an old term for "science"). If not, then what are you getting at? If so, do you have source(s) to back this up? This all seems to be getting away from the main issue, which is that any claims about the term's etymology should be (secondarily) sourced – not left to editors to speculate about. –Deacon Vorbis (carbon • videos) 21:24, 21 July 2019 (UTC)

The essential nature of area defining this function was acknowledged by Derek Thomas Whiteside (1961) "Patterns of mathematical thought in the later seventeenth century", Archive for History of Exact Sciences 1(3):179–388, § III.1 The logarithm as a type-function pp 214–231, see especially page 231. — Rgdboer (talk) 23:11, 21 July 2019 (UTC)

@Rgdboer: I don't have access to this source, can you quote the relevant portion(s)? –Deacon Vorbis (carbon • videos) 00:09, 22 July 2019 (UTC)

Deacon Vorbis, a quote is in our article History of logarithms. It seems to me to be about several concepts from analysis and geometry coming together and becoming the natural logarithm, but I don't see any justification to say that the naturalness is inherited from geometry instead of from analysis. We don't call them "hyperbolic logarithms" any more, so it seems to me we are de-emphasizing the relation to geometry these days. —Kusma (t·c) 10:31, 22 July 2019 (UTC)

Mmm, okay, and yeah, I managed to ... "find" ... a full copy, and there's really no discussion on why the term is appropriate, or who first used it, etc. So barring any other sources, I'm not sure there's anything to do here. –Deacon Vorbis (carbon • videos) 13:33, 22 July 2019 (UTC)

The section has been restored with citation from V. Frederick Rickey who explicates Euler's development of the subject. — Rgdboer (talk) 22:11, 26 July 2019 (UTC)

@Rgdboer: The source you cited merely says that Euler called it by "natural or hyperbolic", not any of rest of that, or why he chose the term "natural" (was that term already in use? did Euler coin it?). I'm sure that a brief mention of Euler in the history section would be fine, but not any of the big pile of OR that was the main concern. –Deacon Vorbis (carbon • videos) 22:44, 26 July 2019 (UTC)

"Big pile of OR" should be described as 270 years have passed since Euler: anything original on this topic is unlikely. — Rgdboer (talk) 22:53, 26 July 2019 (UTC)

@Rgdboer: Are you talking to me? I'm guessing so, but you didn't indent your reply (I've done so for you), or give an actor for should be described, so it's hard to be sure. Anyway, I'm not sure what else I can do here. Nowhere in the section was there really an explanation of the origin of the term natural logarithm, and what was there wasn't sourced, so I don't understand what you're looking for here. –Deacon Vorbis (carbon • videos) 00:58, 27 July 2019 (UTC)

e^-lnx

Should we not include the line:

e^-lnx = 1/x

? — Preceding unsigned comment added by 2603:6011:3140:7400:B4A0:B8CE:398B:B46E (talk) 03:52, 12 March 2021 (UTC)

Absolute values in logarithms

(Moved the following unsigned comment by User:David phys davalos from my talk page).--Sapphorain (talk) 00:10, 9 July 2021 (UTC)

The antiderivative of 1/x is not log(abs(x)), is simply log(x), please do not undo my changes. (Unsigned comment by User:David phys davalos)

Both ln|x| and ln(x) are antiderivatives of 1/x for x real and nonzero. But as at this point of the article the function ln(x) is only defined as a real function of the real positive variable x, we better stick to the former.--Sapphorain (talk) 00:10, 9 July 2021 (UTC)

Observe that if you are taking only x>0, abs(x) is precisely not needed, it introduces confusion since log(x) is in general different from log(abs(x)). I agree that they are the same for x>0, therefore you do not need the absolute value. The confusion is introduced because log(|x|) can be trivially extended for all real x (and real-valued), while log(x) does not enjoy such property. Moreover, is log(x) what is eventually extended, not log(abs(x)). In summary, as you said abs(x) does nothing, so let's make things simpler. — Preceding unsigned comment added by David phys davalos (talk • contribs) 20:41, 9 July 2021 (UTC)

In fact, observe that using the uneded abs(x) introduces inconsistencies when dealing with trigonometric functions, giving rise to functions defined in domains that they shouldn't be. I encourage you to leave things simpler (and in fact, correct).

I reverted you. Things are not simpler when they involve undefined notions, they are just not anymore understandable. --Sapphorain (talk) 21:27, 9 July 2021 (UTC)

Wow, wait, what notion is not defined?. You are making things involved since you are confusing domain issues with the function itself. Please provide a reference of your highly non-standard and non sense rules. — Preceding unsigned comment added by David phys davalos (talk • contribs) 23:18, 9 July 2021 (UTC)

If you do not want to 'believe' me, believe Wolfram: https://www.wolframalpha.com/input/?i=int%281%2Fx%2Cx%29 — Preceding unsigned comment added by David phys davalos (talk • contribs) 23:22, 9 July 2021 (UTC)

And: https://www.wolframalpha.com/input/?i=int%281%2Fabs%28x%29%2Cx%29

Now, please, let's stop this annoying game. You already said that for x>0 abs(x) does nothing, and the article is about x>0, abs(x) is totally not needed! and introduces confusion for the reader that eventually reads complex logarithms. — Preceding unsigned comment added by David phys davalos (talk • contribs) 23:26, 9 July 2021 (UTC)

At this point of the article, $ln(y)$ is defined exclusively for a real positive argument, as a real function. For a value of $x$ such that $y=\sec(x)$ is negative, for instance, $ln(y)$ is undefined.--Sapphorain (talk) 06:22, 11 July 2021 (UTC)

Confusion

As a non-mathematician, but engineer, this article is somewhat confusing. It indiscriminately mixes chat about any base logarithms in with that of the natural base logs, instead of focusing on the natural logs and how they are different from the others. It's missing what I recall as the defining characteristic of the natural logs: "But the one property that goes to the essence of e and makes it so natural for logarithms and situations of exponential growth and decay is this: d(e^x/dx) = e^x." 74.127.200.33 (talk) 18:45, 11 October 2022 (UTC)

Absent Axes

The graph on the right illustrating the curve has two axes. It is conventional and important for clarity to label axes. The axes on this graph are unlabelled, making it confusing to the non expert reader. The expert reader does not need to read this article, so it is necessary to clarify thing like this. — Preceding unsigned comment added by 209.93.146.80 (talk) 20:26, 4 February 2023 (UTC)