Talk:Logarithm/Notation

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This is an archived discussion of logarithm notation. Add any new bugged me for a long time, because people even use log in the statement of the prime number theorem without saying which base they're using!

I would hope that in the wikipedia, we always use ln for the natural logarithm; the other two, when they are needed, should be accompanied with a half-sentence explanation.

And yes, I think this is definitely worth mentioning. --AxelBoldt

Using "log" with no subscript to mean base-10 logarithm, is engineer's notation whose justification is obsolete. Mathematicians nowadays use either "log(x)" or "ln(x)" to mean loge(x). I prefer the former notation. Michael Hardy 22:16 Jan 26, 2003 (UTC)

But that former notation will confuse all but the most hardcore mathematicians. I'm sure there are more engineers among our potential readers than mathematicians, so it seems prudent to use a notation that's unambiguous for both groups. AxelBoldt 02:52 Jan 28, 2003 (UTC)

I'm a mathematician and I use ln exclusively. I never use log by itself at all, although I sometimes write log10. Loisel 02:54 Jan 28, 2003 (UTC)

If I am wrong tell me but isn't natural logarithm is an inverse function of expotential function? -- Taku

If you look again, that's the first phrase of the article.

The first phrase says logarithm is an inverse funcion of expotential function. And my question is natural logarithm is an inverse funcion of expotential function. Am I mistaken?
Somewhat confusingly one speaks of the exponential function, meaning e^x, and an exponential function a^x. The inverse funcions are the natural logarithm and the logarithm to the base a, respectively - Patrick 21:24 Jan 28, 2003 (UTC)

Also, the following comment, aside from not being in english, is impertinent:

In computer science, logarithm is used for explaning logarithmic algorithm such as binary search, implicitly assuming the base of logarithm functions is 2.

At the limit, one might add that the base 2 logarithm is sometimes the default one in some computer science texts. Loisel 03:10 Jan 28, 2003 (UTC)

What do you mean by impertinent? Just a few sentences don't hurt the article.
See Michael Hardy's comment below. And, if we pollute the article with snippets of little relevance without any structure, the article becomes impossible to read. Conciseness is a virtue. Loisel 03:33 Jan 28, 2003 (UTC)

I disagree. First of all, the encyclopedia is not a textbook for math classes. The purpose of the article should not only teach about logarithm in pure math term but also mention about usage, even mis-usage. In computer science, the term logarithm pops up and is used with the base 2. I think the article is slightly targeted for math geeks. I think it is more appreciate to mention more about less math-like stuff for general audience -- Taku 03:41 Jan 28, 2003 (UTC)

In any case, the information is already contained in this sentence, taken from the article In most pure mathematical work, log is used to denote loge, in most engineering work, it means log10, while in information theory, it often means log2, which also sometimes is written as lg.
Also, there's no need for name calling. Loisel 03:46 Jan 28, 2003 (UTC)

Why can't we simply use a term computer science or logarithmic algorithm? And also is the sentence like "Whenever a possibility for ambiguity exists, this ambiguity should be resolved by explicitly writing out the base." Point of view? I agree with such a practice but ther is not need to say. -- Taku

Someone made a nonsensical assertion that nowadays the main use of logarithms is solving equations in which the unknown is in the exponent. I deleted it. Of course, if that were true, then no one would ever think about base-e logarithms, nor differentiate logarithmic functions. This raises a question: If someone reading this page wants to know what logarithms are used for, we could include some material responding to that. That would be a fair amount of work, and I have other things to do, but may a list of links to articles that exhibit examples of the use of logarithms could serve. One such article is Prime number theorem. Surely we could find a variety of such topics. Probably some of them would be on number theory, some on probability, some on analysis of algorithms, some on differential equations of physics, some on information theory, some on entropy in physics, etc. Michael Hardy 03:27 Jan 28, 2003 (UTC)

Also, an extensive "related applications" section can be added to almost all articles in wikipedia, and then you can make all articles three times as big. I don't think that's a good thing. A short, bulleted list might be acceptable, but I would advance with care. Loisel 03:35 Jan 28, 2003 (UTC)
On the other hand, for those with less mathematical background (who might be most likely to consult an article like this one!), we might want to add a paragraph that gives people an idea of why the log idea is useful in general. In a way, "compunded percentage growth" is a kind of log concept; perhaps there is some similar, common analogy that can help explain why log is interesting to mathematicians, engineers, computer scientists, physicists, etc. I'd be more interested in seeing a (short!) paragraph about this kind of thing before how it's used by, say, number theorists. Chas zzz brown 08:15 Jan 28, 2003 (UTC)
I have tried to write the beginnings of such a paragraph. Contrary to Mike above, I do think that logarithms are often used to "solve equations where the unknown appears in the exponent", i.e. to invert exponential functions. Then ln often shows up because its derivative is 1/x, and it is therefore the integrals of 1/x. Maybe we should also mention logarithmic scales widely used in the sciences (pH, dB) and coordinate systems with logarithmic axis scales. Any other things? AxelBoldt 17:31 Jan 28, 2003 (UTC)
I never said logarithms are not used that way; I said it is nonsense to say that that is the main use of logarithms. Michael Hardy 18:32 Jan 28, 2003 (UTC)
link to put in article: Logarithmic measure

You might be interested in seeing the discussion at Talk:natural logarithm. Here is a possible solution that I think is best, although I suspect that most people here will not agree.

First, everyone agrees that "ln" stands for natural log. Even people who don't use the "ln" notation recognize it as such, it poses no misunderstanding, even if very few people (e.g. in mathematics) use it. So, "ln" should remain an accepted usage.

However, the "log" notation appears to have mutually conflicting meanings among different groups of people, and within these groups of people, the usage is fairly standard, common, or at the least, assumed by default. Among mathematicians and many scientists, it's assumed to be natural log, and it is the primary notation used in math for this function (far more than "ln"). Among engineers and others, "log" apparently means log-base-10, and this is assumed to be the default meaning of the notation. And among computer scientists or algorithic analysts, "log" is often taken to mean log-base-2, for a variety of theoretical and practical reasons (log-base-2 naturally (no pun intended!) arises out of the study of algorithms and so forth, in this sense it has a true significance that is not just arbitrary).

Forcing a standard meaning of "log" for all wikipedia users has the effect of alienating the other groups (at least 2 other groups) and it forces them to give up the notation that is standard in their disciplines. Forcing "log" to mean log-base-10 forces mathematicians to give up a notation that is standard and used by 95% of the people. Forcing "log" to mean natural log forces engineers, many scientists, and others to give up being able to use "log" for log-base-10 without specifying the base. (Apparently, advocates of "log" for log-base-10 fail to consider that using "log" in this sense is also using "log" without specifying a base, just like mathematicians use "log" for ln without specifying a base, so the argument that it's bad because "the base isn't specified" is wrong, or at least, this argument can just as well be applied to the common logarithm to argue that people should never use "log" without putting the base 10) Forcing "log" to mean base 2 would be pleasing to computer scientists and so on, but would force mathematicians and scientists to both give up their notation. ANY mandate on the meaning of "log" necessarily forces LARGE numbers of people to give up standard notation. Saying that "log" should be log-base-10 because "more people coming here will be engineers than mathematicians" seems disingenuous and a bit insulting.

So, one possible solution is that the meaning of "log" would not be mandated to any specific meaning, and whenever an article uses "log" without a base, a small line at the top of the article in small font could specify the notation used in that article, with appropriate links to explain the issue. The use of "log" MUST be constant throughout an article, however. And, of course, if someone wants to specify a base explicity, or use "ln", this is perfectly fine. But the "log" notation is used in too many different ways by too many different people.

This solution has the downside that people will not know the meaning of log without looking at the top of the article. BUT THIS PROBLEM ALREADY EXISTS AS THE SITUATION STANDS -- MATH PEOPLE ASSUME IT'S NATURAL LOG AND GET CONFUSED WHEN ENGINEERS AND COMPUTER PEOPLE USE IT DIFFERENTLY, ENGINEERS ASSUME IT'S BASE 10 AND GET CONFUSED WHEN MATH PEOPLE USE IT DIFFERENTLY, AND SO ON AND SO ON. The problem ALREADY EXISTS. Forcing a particular meaning is basically saying, "well, we took a vote, and this many people won, so that's it; everyone else has to adjust". With the solution above, people simply have to be aware of the policy (stated at the top of the article) and then the inconvenience is spread more evenly among the different people who use this notation.

In computing, I've seen lg, or the base is shown explicitly as log2.
A more flexible solution is the one that people do most commonly in writing; for example "log ... where log is the natural logarithm/where log is the base-10 logarith" Dysprosia 22:56, 8 Oct 2003 (UTC)