Talk:Logarithm

Link in Computer Science section

Does a major part of the whole sentence need to be linked to the change of base identity in this section? I've edited it so only the 'following identity' text is linked; can someone please change this back if the original was better? Thanks. Dakuton (talk) 21:19, 28 October 2009 (UTC)

Tables of Logarithms

I think this section should be moved to a separate page and expanded. Mathematicians who have been educated in the last 30 years have never seen a table of logarithms because they have been replaced by electronic calculators. The history of the availability of tables of various number of decimal places should be traced. The historical effects of their invention and use in astronomy cannot be overemphasized.

Trojancowboy (talk) 19:47, 5 February 2010 (UTC)

Difference of root and reciprocal

I was bored one day, I was playing around with the ln(x) function on a piece of graph paper and a calculator. :-P I noticed an unusual property: $Log(x)=\lim _{n\to \infty }n{\frac {x^{1/n}-x^{-1/n}}{2}}$ I've checked many different places and verified it. I can't find anyone else mentioning this property, either. Should it be included on Wikipedia? I think it probably should be, but I can't find a good place to slip it into the article... Timeroot (talk) 05:43, 14 February 2010 (UTC)

Let's see - for a fixed value of x:

$x^{1/n}=e^{\ln(x)/n}=1+{\frac {\ln(x)}{n}}+O(1/n^{2})$

$x^{-1/n}=e^{-\ln(x)/n}=1-{\frac {\ln(x)}{n}}+O(1/n^{2})$

$\Rightarrow n{\frac {x^{1/n}-x^{-1/n}}{2}}={\frac {n}{2}}\left({\frac {2\ln(x)}{n}}+O(1/n^{2})\right)=\ln(x)+O(1/n)$

$\Rightarrow \lim _{n\to \infty }n{\frac {x^{1/n}-x^{-1/n}}{2}}=\ln(x)$

To include this in the article, you would need to find a reliable source for this limit. Without a reliable source, it is original research. Gandalf61 (talk) 09:46, 14 February 2010 (UTC)

What's the name for the argument of the logarithmic function?

When reading the exponential term a^x, one can say "exponentiation - of a - to the exponent n". However, one can also use the explicit name "base" for a, and say: "exponentiation - of the base a - to the exponent n". My question is about whether one can also use any explicit name for x - when reading the logarithmic term log_ax, i.e. by saying something like: "logarithm - of the blablabla x - to the base a"...

HOOTmag (talk) 20:47, 15 February 2010 (UTC)

Change of Base section

I didn't find the change of base section clear enough to be fully understood. I have found a simpler proof here [1].(includes proofs for the other 3 laws of log) Mohamed Magdy, Thank You! (talk) 20:53, 25 February 2010 (UTC)

The "simpler proof" on that web page is actually the same proof that's given in the "change of base" section of this article. Michael Hardy (talk) 23:07, 25 February 2010 (UTC)

Properties of Logarithms

Some of the properties of Logs are not entirely correct.

Log(AB) does not only equal Log (A) + Log(B) (This is only a special case, when both A>0 and B>0).

The general property is Log(AB)= Log |A| + Log |B|. This is because both A and B can be less than 0.

Why is this not in the article?

Another property of Logs that is missing is the following:

Log to the base b^x (A^y)= (y/x)• Log to the base b (A) David Yakubov (talk) 05:11, 4 March 2010 (UTC)

"Why is this not in the article?" Probably because no one has incorporated it yet. As for your first point, how does this look to you:

An important feature of logarithms is that they reduce multiplication to addition, by the formula:

$\log(xy)=\log |x|+\log |y|\,.$

That is, the logarithm of the product of two numbers is the sum of the logarithms of those numbers' absolute value.

My understanding of the topic is meagre at best, and I see some potential for complication here, so I'm not incorporating this into the article myself – please correct or improve as necessary here or fix the article directly. Be bold! /ninly_(talk) 13:53, 4 March 2010 (UTC)

The wording could be tightened up but the way to do that is to make it clearer that this article in the main only deals with positive real numbers. No absolute values should be put in - the equations don't need to be changed. There is a small section on the logs of negative and complex numbers which points to another article. Dmcq (talk) 15:04, 4 March 2010 (UTC)

If x, y > 0 then

$\log x+\log y=\log(xy).\,$

That's the essential idea one should convey. One could mention the corollary in an appropriate context, but it shouldn't have anywhere near as much prominence as this main idea. Michael Hardy (talk) 16:06, 4 March 2010 (UTC)

A more fundamental answer would be: the formula $\log(xy)=\log |x|+\log |y|\,$ is not in the article because it is not generally true. It fails for example if x>0 and y<0. It is possible to extend the logarithm to the complex numbers (excluding 0), albeit it as a multivalued function. For that function $\log(xy)=\log x+\log y\,$ for all values of x and y unequal to zero (seen as multiset). For most values of x and y, the equation stated above (with the absolute values) is not true. −Woodstone (talk) 16:35, 4 March 2010 (UTC)

The numbers in discussion here are the real, and not any other set of numbers. Of course the property fails for x>0 and y<0, because for the reals, both x and y (or any even amount of variables) have to either all be positive or all negative, for the property to remain true.

Another important property not listed in the article is this one:

• ${\log _{a^{q}}{b}}^{p}={\frac {p}{q}}\log _{a}{b}$

List of Properties

• $\log _{a}(bc)\ =\log _{a}|b|+\log _{a}|c|\quad (bc>0)$

• $\log _{a}{\frac {b}{c}}=\log _{a}|b|-\log _{a}|c|\quad \left({\frac {b}{c}}>0\right)$

• $\log _{a}(b^{p})=p\ \log _{a}|b|\quad (b^{p}>0)$

• $\log _{a^{k}}b={\frac {1}{k}}\log _{a}b$

• ${\log _{a^{q}}{b}}^{p}={\frac {p}{q}}\log _{a}{b}$
• $\log _{a^{k}}b^{k}=\log _{a}b$
• $\log _{a}b={\frac {\log _{c}b}{\log _{c}a}}$

$\log _{c}a^{\log _{a}b}=\log _{c}b\Leftrightarrow \log _{a}b\cdot \log _{c}a=log_{c}b\Leftrightarrow \log _{a}b={\frac {\log _{c}b}{\log _{c}a}}$

• $\log _{a}b={\frac {1}{\log _{b}a}}$
• $a^{log_{c}d}=d^{log_{c}a}$

The Russian article on Logarithms has all the properties as well as many of their proofs.

David Yakubov (talk) 01:57, 5 March 2010 (UTC)

As stated before, the equation:

log ab = log a + log b is more generally true than

log ab = log |a| + log |b|

This more complex and less valid formula does certainly not belong in the lead section. −Woodstone (talk) 07:11, 10 March 2010 (UTC)

...and all the other properties there are easily derived from three basic ones (change of base, exponent->coeff, coeff->addend), and still many of them only work once restricted to positive/integer numbers only. —Preceding unsigned comment added by Timeroot (talk • contribs) 23:23, 24 March 2010 (UTC)

apropos history section

Please re-read the section which you re-inserted - it talks about the etymology of the term "algorithm" and also has justification being placed in an article about the history of algebra. It does not fit here.
The term "logarithm" has other etymological roots.
217.236.174.10 (talk) 15:35, 10 April 2010 (UTC)
PS Of course we could copy-paste the history section of the mathematics article - but it would not make much sense, would it? 217.236.174.10 (talk) 15:40, 10 April 2010 (UTC)

Information & complexity

"with k bits (each a 0 or a 1) one can represent 2^k distinct values, so any natural number N can be represented in no more than (log_2 N) + 1 bits."

Natural number is an ambiguous term. According to that article, it may or may not include 0. While "no more than" covers both cases, wouldn't it be clearer to chose one definition, either positive integers or non-negative integers? Thus:

"so any positive integer N needs (log_2 N) bits to represent it."

or

"so any non-negative integer N needs (log_2 N) + 1 bits to represent it."

Dependent Variable (talk) 07:53, 12 May 2010 (UTC)

Go ahead! (I would prefer the first of the two). Jakob.scholbach (talk) 11:47, 12 May 2010 (UTC)

However, how do you represent N=1 in zero bits? Perhaps you mean to say that log₂ N bits are needed to encode all integers from 1 to N (inclusive)? Then (1) carries no information, 0 bits, for (1,2) you need 1 bit, for (1,2,3) 2 bits. You should indicate the rounding up of the value explicitly. −Woodstone (talk) 12:16, 12 May 2010 (UTC)

It could be phrased a bit better. The number N can be represented using 0 bits if we know in advance that's the only number that could be used in a context. For instance the answer to how many side has an octahedron needs zero bits to represent it. What's meant is that any number in the range 0 to N can be represented using that number of bits. Dmcq (talk) 13:13, 12 May 2010 (UTC)

That does not address all concerns. To encode N items, the number of bits needed is log₂ N rounded up to the nearest integer. −Woodstone (talk) 05:58, 14 May 2010 (UTC)

Sorry, I'm new to the wiki, I edit the article in a way adresses all concerns but as I couldn't believe the situation before I edit, I started to investigate the history. Both my edits about base (unnecessary and inconsistent concerns about "zero") and guaranteeing an integer value was in the history. I know these are elementary stuff. So maybe there was an argument about it and I missed? —Preceding unsigned comment added by Oz an (talk • contribs) 01:41, 7 July 2010 (UTC)

Antilogarithm

I refer to the statement within the article:

"At first, Napier called logarithms "artificial numbers" and antilogarithms "natural numbers". Later, Napier formed the word logarithm to mean a number that indicates a ratio: λόγος (logos) meaning proportion, and ἀριθμός (arithmos) meaning number. Napier chose that because the difference of two logarithms determines the ratio of the numbers they represent, so that an arithmetic series of logarithms corresponds to a geometric series of numbers. The term antilogarithm was introduced in the late 17th century and,

while never used extensively in mathematics, persisted in collections of tables until they fell into disuse."

This is just not true. To obtain a mathematical solution using a Log table the Antilog has to be used to provide the end result from the logs. So Antilogs are an interegal part of using Logs. Thus they can never not be used.

In fact even today there are no spreadsheets programs that provide both an @ function for Logs and an @ function for Antilogs. Consequentally one is left with having to use printed log tables to produce the Antilog solution, since the production of logs is useless without the antilog. —Preceding unsigned comment added by P. Dickins (talk • contribs) 09:58, 7 July 2010 (UTC)

I don't know what you mean by an @ function. You weren't looking for 'antilog' were you?, you just use 10^x or exp(x) for that. With the printed logs it is perfectly easy to do ones work just using the log table to do antilogs. Dmcq (talk) 10:16, 7 July 2010 (UTC)

General logarithmic function

By looking at the article, one may notice that it follows the traditional way of defining a logarithm and like so many texts, it does not include the definition of the exponent being irrational. So many texts just assume that the base to a power is defined for the base greater than zero and the exponent is any real number and the usual laws of exponents are valid that it looks the Wiki article just wants to follow suit. If so, fine. However, there is a general formula that applies to any exponent, real number (rational or irrational) and to any base. Neither the Russian nor the German page has it. Perhaps the French...JDPhD (talk) 21:44, 19 July 2010 (UTC)

The majority of textbooks dealing with logarithms are introducing the subject to students so they concentrate on a simple beginning, namely rational exponents. Wikipedia's coverage should also include a rigorous coverage of irrational exponents. If you have a suitable source that you can cite in the article please go ahead and add that rigorous coverage. Dolphin (t) 22:29, 19 July 2010 (UTC)

The new "general" section had no contents, just a reference to an inaccessible book, so I took it out. If there's something that should go there, put it in. It would be nice if there's an online source, too. Dicklyon (talk) 02:50, 22 July 2010 (UTC)

How about moving section logarithm#Alternative definition via integrals up as general definition? −Woodstone (talk) 03:50, 22 July 2010 (UTC)

Why? The beginning of the article is accessible to schoolchildren without calculus, this would make it inaccessible. This is an encyclopaedia not a calculus textbook. Dmcq (talk) 06:58, 22 July 2010 (UTC)

Also, the Alternative definition via integrals is not the general definition. One thing more, when I began this section that was erased, I was going to include a "hidden comment" asking the editors not to erase it until it's done. For one thing, there will be two sections with two drawings and the references but the whole thing cannot be done in a jiffy. The book that Dicklyon mentions has ISBN for the new editions; the one cited in the article happens to be the edition of 1959. So if the rest of you feel ok with a "hidden comment" (not to erase anything until it's done) I'll go right ahead and start. I promise you, you won't be sorry. JDPhD (talk) 19:14, 22 July 2010 (UTC)

It's probably best to prepare something like that first in a user sandbox until you have enough to look reasonable if its going to take some time. If you want to develop in an article putting in the citations and basic discussion first and doing the tidying up of the language later is less likely to get removed. Dmcq (talk) 20:49, 22 July 2010 (UTC)

I agree that using a personal sandbox is the best way to develop extensive changes to any article, especially as no-one will interfere with your changes while they are work-in-progress on your sandbox. Information about creating a personal sandbox is available at WP:SP and WP:USERSUBPAGE. Dolphin (t) 23:14, 22 July 2010 (UTC)

By "inaccessible" I meant I can't find access to the book contents online, so can't see what you're getting at and try to help. Surely there are other books, accessible on amazon or google, that could be used as source for what you're trying to do, yes? Dicklyon (talk) 02:46, 23 July 2010 (UTC)

As alternative to sandbox, you could post your proposed new section here on the talk page, and invite help to get it into good enough shape to put into the article. Nothing is lost, by the way; just use the history to go back to your version, or the corrected one after it, and edit to copy out the section source that you want to reuse. Dicklyon (talk) 02:49, 23 July 2010 (UTC)

OK let's try it out first, here in the Discussion page. Of course, help is always welcome.JDPhD (talk) 19:46, 23 July 2010 (UTC)

The general expression of the logarithm

So far in this article, the function $y=a^{x}$ has been defined only for rational values of "x", except in the particular case when $a=e$. We shall now consider the case in which "a" is any positive number.JDPhD (talk) 20:13, 23 July 2010 (UTC)

There's the following obstacle to continuing. From now on, in the proposed addition, everything except the two diagrams is original research. It is rather difficult to find references to match the original research. Therefore, it does not satisfy Wikipedia standards. So, let's fold the page here and desist from the enterprise.JDPhD (talk) 18:58, 26 July 2010 (UTC)

That sounds like the right decision. Dicklyon (talk) 00:26, 27 July 2010 (UTC)

Simplification

This recent edit "simplified" the proof that the real log is well-defined. Actually I just wrote this elongated explanation in order to make it accessible to people who don't know about (inverse) functions etc. I'm going to revert that simplification unless somebody convinces me of the contrary. Jakob.scholbach (talk) 13:42, 1 August 2010 (UTC)

Thinking about it again, I decided to revert this for the moment. Jakob.scholbach (talk) 13:51, 1 August 2010 (UTC)

I simplified your explanation because I don't see the point of this lengthy discourse on a special case of a more general result. The general result - a continuous strictly monotonic real-valued function has an inverse - is both intuitively obvious and simple to prove rigorously. The fact that the exponential function has an inverse for b ≠ 1 is not surprising, and not worth writing paragraphs about. Wikipedia is not a textbook - "The purpose of Wikipedia is to present facts, not to teach subject matter". Gandalf61 (talk) 14:21, 1 August 2010 (UTC)

I'm aware of wp:nottextbook and I agree my draft so far is somewhat borderline. The problem with your approach is that it is practically unintelligible for a 15, 16 year high-school reader, which is the audience we should care about at this point. I tried to avoid the words "function", "continuous", "monotonic", inverse function, since these words will not be known to this audience. Right? So the question is: how can we give a meaningful explanation, which is accessible to a broad audience, yet stay simple and concise? How about a little animation depicting the situation (think of a graph and repeating this bisection process a few times)? Jakob.scholbach (talk) 14:48, 1 August 2010 (UTC)

A minor WP:MOS thing: "we" is unencyclopedic language. Mathematicians (including myself) have certainly a reflex of talking to the reader... Jakob.scholbach (talk) 14:48, 1 August 2010 (UTC)

Your explanation is neither simple nor concise nor complete. For example, you do not explain why your bisection process converges to a limit - you are implicitly using the completeness of the reals here. Any reader bright enough to wonder whether the exponential function really has an inverse is going to wonder about this too. A simple and concise explanation will use the correct and accurate terminology, not baby words like "bigger and bigger" and "closer and closer". The interested reader can look up the linked articles, and will then have learnt something. I have restored my simplified version, modified to avoid the use of the second person. Gandalf61 (talk) 15:12, 1 August 2010 (UTC)

I am the first to agree that my draft is only a humble start (which I hope to improve). Let's, for now, not worry too much about my admittedly childish wording.

The more fundamental question is this: for whom do we want to write this article here? You didn't seem to notice that in the next subsection there is already pretty much what you call the "simplified" explanation using calculus language. (Btw, your version is inaccurate as the strict monotonicity is not enough, the unboundedness to the right and boundedness by 0 to the left is needed). So, for the bright (I would rather say, educated) reader we have this. However, this is one of the 500 most viewed math articles, and >95% of our readers won't know what continuous means. Linking to continuous function, say, directs them to a mess(!), and I dare say nobody who does not already know this notion will dig trough it and come back and apply it to logarithm. Do you agree with that? Jakob.scholbach (talk) 15:42, 1 August 2010 (UTC)

About simplicity: specifically in what way is the more detailed approach not simple? Or the other way round, in what sense is your edit a simplification? (As opposed to replacing, after all, relatively easy facts by more fancy terminology?)

About completeness: I agree that the explanation I put is not 100% waterproof in the standards of a (under)graduate level. But certainly, the completeness of the reals is about the last thing I would care about in the presentation here. Most, say, engineering textbooks would not mention that. The alternative "is a continuous, strictly monotonic function from the reals to the positive reals, so it has an inverse function from the positive reals to the reals" may be more "complete" (granting that the single word so just encapsulates all of these things), but is without any doubt much less understandable. Jakob.scholbach (talk) 15:42, 1 August 2010 (UTC)

I drafted animation illustrating the proof (lots of details have to be improved). Any thoughts about that? Jakob.scholbach (talk) 16:51, 1 August 2010 (UTC)

I must generally agree with Gandalf here, the explanation is actually looking like a week case of WP:OR: an uncited proof. It show the problems of such with a lack of mathematical rigor, and an unconventional treatment of the material, Spivac for example defines the log of a real number through the evaluation of an integral. I do feel this section would be better treated by referring to the appropriate theorems. I'm not convinced by the need for a layman's explanation, we are considerably far down the article in a section about Analytic properties so I would expect some level of mathematical soptication by this level, many readers will be happy with just a statement that it can be defined to cover positive reals, by using techniques of analysis.--Salix (talk): 17:50, 1 August 2010 (UTC)

Log functions graph

Nice article :) Just one question in passing: why base 1.7 in the log functions graph? It seems an unusual choice of number - is this purely to give visual symmetry around the ln curve or does it have some interesting mathematical property? EyeSerene^talk 13:06, 2 August 2010 (UTC)

I believe 1.7 was chosen purely to provide visual symmetry. It needed to be a number between e (2.718...) and unity (one). The number 1.7 is not the arithmetic mean of 2.718 and 1.000, but it does provide good visual symmetry. Dolphin (t) 13:39, 2 August 2010 (UTC)

Yes, it does. The only thing I could think of (numerically) was that the dB scale is a log scale, 3 is a doubling of power/intensity on this scale, and 1.7 is close to √3... but that did seem a bit tenuous :) EyeSerene^talk 13:45, 2 August 2010 (UTC)

History of the logarithm

I find with certain surprise that it was not Napier who discovered logarithms, but an unknown indian mathematician in the 8th century!! Although the sources clearly state it, I have my doubts. Indian writers are known for their nationalistic bias, driven by the need to boost indian national pride. In an attempt to counterbalance what they see as "Eurocentrism", they created another ethnocentrism called "Indocentrism". Just look at the various claims that 14th indians invented calculus 300 before Newton and Leibniz, just because some calculus related ideas are found in thei works (forget Archimedes and the other greeks who did similar works 1500 years before). Other known cases include the discovery of heliocentrism by astronomer Ayharbata, and the determination of the speed of light by Sayana, a commentator of the Vedas (don´t ask me how he did it, not even Subhash Kak knows).

So far, I have only seen this claim in Jain run websites, (which I don´t think are very reliable) and the works of R.C and A.N. Singh and Gupta. No other scholar working in the field of indian matehmatics ever mentions that they worked with logarithms before Napier. Can we ignore 100 works who don´t mention this, and listen to these 2? --Knight1993 (talk) 20:55, 11 August 2010 (UTC)

I've looked into the source and there is good evidence that they did study the process of "how many times can you halve a number". The A.N Singh references is basically a direct translation of the original text. You do need to be very careful with the claims, they did not invent our modern conception of logarithms, from the text it only seems that it was applied to integers, and chiefly as a way of looking at very large numbers. No evidence that it was used as a easy way to carry out multiplications, or many of the other applications.

The evidence for the logarithm precursor is much stronger than the speed of light claim, there are several formula for properties of the logarithm precursor spanning several . For the speed of light it just seems to be one sentence with a number which happens to be the approximate value.

So Napier is the discoverer of logarithms, but an Indian did look at something similar before hand. --Salix (talk): 22:21, 11 August 2010 (UTC)

M Stifel did a similar thing, in that he made a sequence of integers aligned with a sequence of powers of two. But if you look at the refs I added, you'll see that historians don't really regard that as a discovery of logarithms. There may be lots of other things in exponential or logarithmic relationship that others have commented on, but I don't think we can add all these as discoveries of logarithms. Dicklyon (talk) 04:02, 12 August 2010 (UTC)

Date of log x (base e) to log x (base 10) and ln x (base e) notation switch?

I've always been under the impression that log x, implied base 10, and ln x, implied base e; but as I have come to find, in the year 1900, log x implied base e. Does anyone know in what year the official switch occurred? I'm trying to dig out the history of how the notation for the Boltzmann entropy formula switched from S = k log W (1900) to S = k ln W (modern). --Libb Thims (talk) 10:49, 2 September 2010 (UTC)

I'm not sure there was a such a switch. There are (still, so to say) areas which write log for base e, as noted in the article. Jakob.scholbach (talk) 14:45, 2 September 2010 (UTC)

Different authors use different notation. I doubt there was ever an official position, or an international decision to switch from one notation to another. Dolphin (t) 22:46, 2 September 2010 (UTC)

There's no such thing as such an "official switch"; there are only conventional usages. There is no authority that issues decrees about such things. "log x" means the base-e logarithm of x when that notation is used in contexts where that is the appropriate base. That is commonplace usage among mathematicians today. In the present day, the "ln x is also used. Not so many years ago, I used to tell people that "ln x" is used only in textbooks for first- and second-year calculus, whereas adults write "log x" for natural logarithm of x. In Paul Halmos' autobiography, he ridiculed the "ln" notation then (in 1984)) appearing in those low-level textbooks, saying no mathematician had ever used it. That was a bit of an exaggeration at the time it was published, and is not true today. But "log x" continues today to be understood as logarithm to the appropriate base, where the appropriate base varies with the context. Michael Hardy (talk) 22:49, 2 September 2010 (UTC)

At Natural_logarithm#Notational_conventions we find this:

Mathematicians, statisticians, and some engineers generally understand either "log(x)" or "ln(x)" to mean log_e(x), i.e., the natural logarithm of x, and write "log₁₀(x)" if the base 10 logarithm of x is intended.

Some engineers, biologists, and some others generally write "ln(x)" (or occasionally "log_e(x)") when they mean the natural logarithm of x, and take "log(x)" to mean log₁₀(x).

In most commonly-used programming languages, including C, C++, SAS, MATLAB, Fortran, and BASIC, "log" or "LOG" refers to the natural logarithm.

In hand-held calculators, the natural logarithm is denoted ln, whereas log is the base 10 logarithm.

In theoretical computer science, information theory, and cryptography "log(x)" generally means "log₂(x)" (although this is often written as lg(x) instead).

Michael Hardy (talk) 22:55, 2 September 2010 (UTC)

Ludwig Boltzmann tombstone, built in circa 1935.

In 1901, Max Planck used the following logarithm notation.

$S=k\log W\!$

This notation convention was engraved, in circa 1835, on Ludwig Boltzmann's tomb (adjacent), a tribute to his 1872 paper “Further Studies on the Thermal Equilibrium of Gas Molecules”, in which he is said to have introduced a variation of this equation (I still have yet to read this paper, being that no readily available English translations exist). It seems, however, that in the years 1930 to modern, the "ln" notation has come into popularity, e.g. 1996 book cover, Crease's 2004 list (see "Equation" section) of the 20-greatest equations ever, etc.,

$S=k\ln W\!$

I have always been a bit puzzled why these two different notations are used. On Wednesday, someone commented to me about this matter:

"The use of "log" refers to (and always did) the natural logarithm (base e) in this formula, and it was only afterwards that log was used to denote the base 10 logarithm and ln the base e."

I'm guessing that some modern writers have tended to switched to "ln" notation, so as to be absolutely clear that base e is the being used, where as "log" leaves the interpretation open to either base e or base 10. I'm sure there's a story as to how this switch occurred. --Libb Thims (talk) 11:39, 3 September 2010 (UTC)

However note that there is a linear relationship between logs in different bases. So the formulas $S=k\log _{e}W\!$ and $S=k\log _{10}W\!$ are equally valid, only they lead to a different numerical value of the constant k. −Woodstone (talk) 11:59, 3 September 2010 (UTC)

My computer is presently operating Microsoft Windows XP. It has a scientific calculator with one button labelled log and another button labelled ln. Dolphin (t) 04:00, 9 September 2010 (UTC)

Path to GA?

I'm hoping to take this article to GA status in the near future. To get a better standing, I'd like to solicit further input of people watching this. What do you think needs to be done before going to GA?

Myself, I see at least the following to-do-items:

• check and substantiate claims in history section
• explain Napier's version of logs more thorougly
• maybe explain discrete logs (a little bit) more. add Zech's logs there
• overhaul the "Calculation" section. What algorithms are used in, say, C++ or Maple for numerical calculations

Jakob.scholbach (talk) 08:50, 26 September 2010 (UTC)

• A minor comment: the complexity theory section jumps rather abruptly to a discussion of fractal dimension. This could use some more exposition. A separate section might even be warranted. 71.182.217.132 (talk) 22:05, 12 October 2010 (UTC)