Wikipedia talk:Featured article candidates/Logarithm/archive1

Comments by TR
more to come.TR 09:44, 22 March 2011 (UTC)
 * References to Wolfram alpha (current refs 29 and 31) should have more description that just "[1]". Note sure what the proper way to reference Wolfram Alpha is, but I think you should be able to use the "cite web" template.
 * Polished the references using Citation template. Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * "Logarithms rely on the notion of powers." That is a very vague (and somewhat weird) statement. Is it really necessary? Looking at the whole start of the section could with a little polishing. (One idea, loose the level heading "Exponentiation", move the sentence "The idea of logarithms is to undo the operation of exponentiation." to the beginning of the section, follow with something like "Exponentiation is a generalization of raising to a power", followed by the current explanation of powers.)
 * I tried this version, but am not satisfied: I believe it is better to separate the reminders on powers and exponentiation and the motivation for log's. The subheadings are supposed to keep the two apart. I'm also no longer fully satisfied with "Logarithms rely on the notion of powers.", but want to say something like: To understand log's you have to know exponentiation, in particular powers. I'm thinking for a good wording for this, but also appreciate your feedback. Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * I think the version you tried was better. Whatever you do the subheading really isn't necessary since it is already the start of a section. (Personally, I really dislike having a subheading directly after a heading.)TR 08:49, 23 March 2011 (UTC)
 * How is this? I really think we should keep the exponentiation separate (ie, as a subsection), since it is might otherwise be confusing what we are talking about. Like this, opening with an example, then recalling the exponentiation briefly and then giving the "abstract" definition, followed by more examples looks more rounded off to me. What do you think? Jakob.scholbach (talk) 22:12, 24 March 2011 (UTC)
 * Could the identities in the "Product, quotient, power and root" be better presented in a table?
 * Good idea. Done Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * The identities section should (IMO) also mention the identity: x=b^(logbx).
 * I think it would be misplaced in that section: the section is concerned with ways to manipulate logarithms. The identity you mention is mentioned further down in section 5.2. Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * Fair enough.TR 08:49, 23 March 2011 (UTC)
 * Maybe change: "Among all possible bases b, that is to say positive real numbers unequal to 1, a few particular choices for b are more commonly used."-> "Among all possible choices for the base b a few are particularly common"? (I don't think the range of possible bases needs to be repeated here, it is in the definition, only a section up. This also avoids the awkward "more commonly used", more common than what?)
 * Good idea. Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * Might want to add sentence why the logarithm base 2 is often (probably because it convenient in binary systems such as computers) used in the section on bases.
 * This is mentioned further down (see Complexity section). I think we don't need to repeat it here. OK? Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * The thing is that you mention 3 types of base that is commonly used. The section explains why two of them are useful, but doesn't mention why the third one is. As small sentence like, "Similarly, base 2 logarithms are convenient when dealing with binary number systems." would alleviate this. You could even add "this is discussed in more detail below" if you want.TR 08:49, 23 March 2011 (UTC)
 * Alright. I mentioned it briefly there. Jakob.scholbach (talk) 19:31, 23 March 2011 (UTC)
 * "In some countries, the notation blog(x) is used instead of logb(x)." Is that really a national thing? The reference only shows an Austrian site using an alternative notation.
 * Reworded. Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * The subsection on complex logarithms should mention and link to the term branch cut. (The concept is currently explained, but it is not mentioned explicitly by name.)
 * Done. Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * "The invention was quickly met with acclaim in many countries." What is the importance of "many countries" here. As far as I know (which in this case is not that far) the scientific community was fairly internationally at the time, making this of little import. Is the intention simply to say that the invention was widely met with aclaim?
 * Sure. Reworded. Jakob.scholbach (talk) 19:31, 23 March 2011 (UTC)
 * Laplace -> Pierre-Simon Laplace (Names should appear in full at the first occurance. Similarly, for Cavalieri, Wingate and Kepler just down.
 * OK. Jakob.scholbach (talk) 19:31, 23 March 2011 (UTC)
 * It isn't clear from the context that the quote from Laplace dates from more than a century after Napier invented logs. It might help to mention a date for this quote.
 * The source does not say when he said that, but I moved the quote down to the phrase about Euler, which are certainly more close. Jakob.scholbach (talk) 19:31, 23 March 2011 (UTC)
 * "Newton's method can also be used to calculate the logarithm, since its inverse function, the exponential function can be computed efficiently." Some explanation of what Newton's method is, seems required.
 * Added a few words. Any more than this should be found in Newton's method. Jakob.scholbach (talk) 19:31, 23 March 2011 (UTC)
 * In the "Arithmetic-geometric mean approximation" subsection, it would be helpful to give an idea what the Arithmetic-geometric mean is.
 * OK, gave a few words. Jakob.scholbach (talk) 19:31, 23 March 2011 (UTC)
 * "The apparent magnitude measures the brightness of stars logarithmically." One sentence paragraph.
 * Glued with the previous paragraph (I don't think we should have more on this here.) Jakob.scholbach (talk) 19:31, 23 March 2011 (UTC)
 * (About log-log plots) "This is applied in visualizing power laws." Not only in visualizing, but also in analyzing power law behaviour.
 * I don't have a very fixed mind on this, but from what I know the interest in these plots is this: given a (statistical, say) datasource, you plot a log-log graph. If you then remark that the points lie on a line you know it is polynomial and you can read off the exponent. Would you call this more than "visualizing"? Jakob.scholbach (talk) 19:31, 23 March 2011 (UTC)
 * Well, this method is commonly used to determine the exponent of a power law. Less so, with the advent of computers that can preform advanced fitting algorithms to fit complicated functions at the touch of a button, but I think it is still regularly used. (I was still taught how to do this in high school in the '90s).TR 08:43, 24 March 2011 (UTC)
 * Alright. I added "and analyzing". Jakob.scholbach (talk) 22:12, 24 March 2011 (UTC)
 * "In thermodynamics, the entropy S of some physical system is defined as" thermodynamics should be replaced by statistical mechanics/physics/thermodynamics, since the given definition is not the definition of entropy from classical thermodynamics.
 * Changed "th." to "statistical th." Jakob.scholbach (talk) 19:31, 23 March 2011 (UTC)
 * References to websites need 1)accessdates 2)Either an author or a publisher.
 * I added the "author" for the two wolfram alpha references. About the accessdates: what particular references do you mean? I prefer not to add accessdates to books.google links, after all these links are just supposed to simplify finding the book and the primary bit of information is the existence of the book. Is this within MOS? Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * See comments below by brianboulton.TR 08:49, 23 March 2011 (UTC)
 * I think I covered the points he raised, but I only have my two eyes. If you see any further problems, please tell me. Jakob.scholbach (talk) 19:31, 23 March 2011 (UTC)
 * Some small reference issues:
 * On small screens (like the netbook I'm posting from) 3 colums become very thin. You might want consider using "colwidth=23em" instead. (The number of columns then becomes dynimical based on the browser width.)
 * The formatting of ISBN numbers needs to be uniformized. I think there are a couple of editors around that have scripts to do this for you. (I think user:Rjwilmsi is one.)
 * The article mixes the use of "citation" and "cite xxx" citation templates (e.g. ref 38 is a "cite book", this leads to inconsistent formatting.
 * Related, most of references do not end with a period, is this intentional?
 * All fixed. As for the periods: unless the reference or footnote contains a full sentence, I did not put a period. (Unless I or someone else made a mistake, but right now I don't see any.) Jakob.scholbach (talk) 23:36, 25 March 2011 (UTC)
 * rest of the references look OK.TR 20:42, 25 March 2011 (UTC)

Comments by Hawkeye
Comments by Hawkeye7 Hawkeye7 (talk) 11:59, 22 March 2011 (UTC)
 * Michael Stifel published Arithmetica integra in Nuremberg in 1544; it contains a table Delete the semicolon and replace "it" with "which"
 * Done. Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * (Joost Bürgi independently discovered logarithms; but published only four years after Napier). No need for the semicolon here (or, for that matter, the parentheses) but you do need a reference to back up the claim. (Consider deleting "only".)
 * All done. Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * Logarithmic function. References required here.
 * Added a reference.Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * Note how log2(n) is within 0.6% of loge(n) + log10(n)
 * To me, this does not seem to be a noteworthy fact. Mathematically, this is an accidental coincidence. From a practical point of view, this is also not noteworthy, since it is not used (or useful) to compute logs. OK? Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * Yes, that is fine. We used to use it a lot back when we still used logarithms. Hawkeye7 (talk) 23:56, 24 March 2011 (UTC)
 * Since we note that log is the natural log in C, it seems fair to note that log10 is the decimal log
 * I prefer not to add this here. The point is that "log" is ambiguous, and is used in that and that domain for this and this logarithm. log10 however, is perfectly clear. If anywhere, this notation should be mentioned in common logarithm.Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * Fine by me. Hawkeye7 (talk) 23:56, 24 March 2011 (UTC)
 * The number e and the modern definition for logarithm Could you expand this?
 * Will think about this. Jakob.scholbach (talk) 18:41, 22 March 2011 (UTC)
 * I've given a little more detail; see also my reply to NW below. Jakob.scholbach (talk) 17:05, 25 March 2011 (UTC)

Oppose by Randomblue
--- I paste here Randomblue's comments from Talk:Logarithm: Jakob.scholbach (talk) 16:03, 28 March 2011 (UTC) ---

-Lead -Later
 * In lead picture, don't use serial comma for consistency
 * The article uses serial commas throughout. (I checked once more and spotted four occasions where no such serial comma was put, this is now made consistent by adding them there.) Jakob.scholbach (talk) 16:03, 28 March 2011 (UTC)
 * Be consistent with "to the base X" and "to base X".
 * I think some variation in language is fine here, but since I'm not a native speaker I'll ask one. Jakob.scholbach (talk) 16:03, 28 March 2011 (UTC)
 * The whole article uses a single variation, with the exception of one occurrence. Might as well be consistent. Randomblue (talk) 02:20, 29 March 2011 (UTC)
 * I find "is written" neater than "is written as" (and in rest of article).
 * Idem. Jakob.scholbach (talk) 16:03, 28 March 2011 (UTC)
 * The sentence "The logarithm of a product of two numbers equals the sum of their logarithms" comes out of the blue. Maybe introduce with "A fundamental property is ..."
 * In the interest of a concise lead section, I prefer not to add this. The new paragraph suggests that something new is being talked about. Thirdly, the following sentence portrays this equation as the "basis for multiplying two numbers", a wording that again underlines the importance of this identity. Jakob.scholbach (talk) 16:39, 28 March 2011 (UTC)
 * Richter scale problem (see above). Another problem is that the Richter scale doesn't "measure earthquakes".
 * Given an earthquake, the Richter scale assigns a number, say 8, to it. What else is this than measuring? Please explain. Jakob.scholbach (talk) 16:03, 28 March 2011 (UTC)
 * Well an earthquake is complex phenomenon with numerous "properties", such as "time", "location of epicenter", "death toll incurred", etc. So what exactly is being measured? Moreover, the Richter scale is a quantifier, not a measurement object; seismometers measure. Randomblue (talk) 02:20, 29 March 2011 (UTC)
 * Maybe this has changed in the meantime, but at least now the lead says "the Richter scale measures the seismic energy produced by earthquakes on a scale". I don't know how this could be more plain. Jakob.scholbach (talk) 17:21, 29 March 2011 (UTC)
 * "The natural logarithm uses the constant e (approximately 2.718) as its base, and is especially widespread in calculus." I would also mention that the natural log is the one primarily used in (pure) mathematics.
 * Good idea. Jakob.scholbach (talk) 16:39, 28 March 2011 (UTC)
 * The fact that the logarithm is a mathematical function (yet even a mathematical object!) is hidden under the rug. This is too much of a dumbing-down.
 * I don't understand your complaint: we have a whole section "Logarithmic function". What exactly do you want? Jakob.scholbach (talk) 16:03, 28 March 2011 (UTC)
 * What I want is that, right from the lead, readers are told the "real" definition as the inverse of the exponential, in parallel to the "dumbed-down" definition given. The words "function", "inverse" and "exponential" really ought to be present in the first few words of the article. Randomblue (talk) 02:20, 29 March 2011 (UTC)
 * Well, "real" is a questionable attribution. Defining the log function is tantamount to defining its values. The lead starts by defining the values of the function, if you prefer this parlance, because this is what the reader needs to know first. The definition we give is in no way dumbed down. It is the same as the inverse function definition, but given element-wise and using a language that is accessible to the targeted audience. Anything like "the log is the inverse function of the exp fct." will be pretty much useless at this point. (The "reality" question lies elsewhere, namely how to define the exponential. This is something we should not/do not/will not discuss in this article here, let alone its lead section.) Jakob.scholbach (talk) 17:21, 29 March 2011 (UTC)
 * Also, note that the last line of the lead does mention the cx. log being an inverse function. That sentence is aimed at an advanced readership, so we can more easily afford such a language. In the beginning, we cannot. Jakob.scholbach (talk) 17:21, 29 March 2011 (UTC)
 * "primarily aids computing applications" -> The untrained eye might find this very confusing, interpreting "computing" as the verb "to compute". Maybe rephrase as "is used in computer science". Also, I don't think that logs base 2 are primarily to "aid computation". They are simply the most natural in the field.
 * Good point. Jakob.scholbach (talk) 16:39, 28 March 2011 (UTC)
 * "Logarithms are commonplace in scientific formulas, measure the complexity of algorithms and of fractals, and appear in formulas counting prime numbers." Remove serial comma for consistency.
 * See above. Jakob.scholbach (talk) 16:03, 28 March 2011 (UTC)
 * "They describe musical intervals, inform some models in psychophysics and can aid in forensic accounting." This seems to be an arbitrary mash-up of examples, which is to me original research.
 * As you may know, there is no book "Applications of logarithms". Therefore, in the strictest sense of the word, any assembly of such applications is original research by synthesis. However, I think you have to counterbalance this strictest possible definition of OR with reality: no article could be written without an editor judging what is important and what is not. In short, your OR accusation is, IMO unfounded an unactionable. Could you therefore make more precise your point: what do you think is under/overrepresented? Jakob.scholbach (talk) 16:03, 28 March 2011 (UTC)
 * I absolutely don't know that there is no such book. You might be surprised, also! Anyway, to be more precise, I find the material too detached and fragmented. In effect, I'm not complaining about what you have selected, but how you present it! Even the little intro to the section is a list of things. As a good way forward, I would rewrite this little intro to show how the topics discussed form a well-chosen, wide ranging selection. I'm simply asking you to subtly disguise the listing. Randomblue (talk) 02:20, 29 March 2011 (UTC)
 * Well, so let me tell you: there is no such book. (Of course, most sources mention two or three app's). I did a lot of literature queries and did not find any comprehensive source mentioning all applications out there. I'm actually not surprised by that, since WP is in a sense quite orthogonal to standard sources of information. Few books take the task of providing a comprehensive picture of one notion.
 * As for "disguising the list": I think what you want amounts to finding a common feature shared by all these applications/occurrences? I doubt though, that such a thing exists: some of these applications stake on log(xy)=log(x) + log(y) in a quite immediate way, others don't: for example, could you tell (and cite) why the log appears in the law of the iterated logarithm? In entropy? In the prime number theorem? Jakob.scholbach (talk) 17:21, 29 March 2011 (UTC)
 * To me, the applications are bluntly presented, one by one, as a list. I don't think I want to find a common feature shared by all these applications, just a more creative way of presenting things. Randomblue (talk) 07:33, 30 March 2011 (UTC)
 * (unindent) I tried my hand at another, more smooth section intro. Do you like this better? (BTW, I think WP:OR is unrelated to a (perceived) lack of creativity in a section intro?) Jakob.scholbach (talk) 19:19, 31 March 2011 (UTC)
 * "The complex logarithm is the inverse of the exponential function applied to complex numbers and generalizes the logarithm to complex numbers." By saying "generalizes the logarithm" here, you are implying that "logarithm" here is defined as the real logarithm. This should be made clear right from the definition, by changing "The logarithm of a number..." to "The logarithm of a real number..."
 * I reworded the sentence you refer to (by removing the word "generalizes"). However, I disagree with putting "real numbers" in the first sentence. Mentioning real numbers in the very first sentence amounts to over-emphasizing their role. After all, the complex logarithm is also an exponent to which the base must be raised. If you interpret group elements as numbers in a wider sense (cf. modular arithmetic), then again the first phrase applies. Jakob.scholbach (talk) 16:39, 28 March 2011 (UTC)
 * I understand your point, and I agree. However, after this first sentence, it should be clear what exactly is discussed. For example, in "The logarithm of x to base b is written logb(x)" I assume the real logarithm is implied. Please be more precise/specific.
 * No. The game is this: you have 2 minutes to tell a 5th grader what a logarithm is. (This time frame corresponds to readling aloud the first paragraph of the lead section, say.) Once he asks you a question, you have to stop talking (=he clicks at a blue link and might never come back, because he is lost). If you would tell: "the log of a real number is ..." he might ask you before you even finish the sentence "but what is a real number?". You stop---before you even told what you can tell (without distorting the truth). Notice that the same might happen when you arrive at "... is the exponent". There though, you have no choice but to let the kid go. The task here is to discern relevant from less relevant. That x is a real number here is factually of little relevance, because, say the group law of logs stays valid (in the cx case in the multivalued sense) in other occasions, for example. Pedagocically it is also less relevant and might even harm our purpose, since most readers won't know what a real number is, let alone what other numbers might be out there. Jakob.scholbach (talk) 17:21, 29 March 2011 (UTC)
 * Wikipedia, as I see it, is not a game or a textbook, and is not aimed specifically at kids. For me, it's an encyclopedia. I guess we see different aims for this article. Randomblue (talk) 07:31, 30 March 2011 (UTC)
 * Yes, it's an encyclopedia, but the encyclopedia has to be accessible to most people. I think using a hypothetical fifth grader is extreme (fifth graders may not even know what exponents are, and defining logarithms is pretty hopeless without that), but most adults should be able to grasp the fundamentals of what a logarithm is and what it is used for. I went only as far in school math as I was required to go, so I think that here I'm a reasonable stand-in for the general public, who mostly did the same. I accept that there are parts of this article that cannot be made comprehensible to me, but I want to understand those fundamentals. And yes, I prefer to do that without having to click away from this article to look up a piece of mathematical jargon whose meaning I half-forgot because I never used it to solve an equation. A. Parrot (talk) 20:51, 30 March 2011 (UTC)
 * (unindent) Could not agree more. Of course, the kid and the game were a metaphor. A. Parrot spelled it out in more concrete terms what I'm thinking. Randomblue, you might also take into account that the lead section is a summary of the whole article. Were the relevant section (section 1) as sloppy as the lead is, your point would be OK. There though, we are as explicit and precise as necessary/possible. I think you just expect too much of a short text. We have to prioritize certain things here, and the real number has lower priority than the "meta" (if you will)-information currently contained in the lead. Jakob.scholbach (talk) 19:19, 31 March 2011 (UTC)
 * "Roughly, a differentiable function is one whose graph has no sharp "corners"." This is too much dumbing down (or plain wrong!) to my taste. The sign function is not differentiable, yet really doesn't have "sharp corners". Randomblue (talk) 00:45, 28 March 2011 (UTC)
 * I changed it to "a cts fct. is diff, if ...", which resolves the "counterexample@ you mention.
 * As for the degree of simplicity, you are entitled to your taste. The choice I see is this: not explain it at all, which would leave puzzled a fair portion of the audience, or explain it roughly (as the phrase explicitly says). We don't have the space to define it here in full fledge, nor should we do this (by WP:SUMMARY or the like). Instead, giving a rough explanation we can hope that the reader is encouraged enough to review/deepen his/her knowledge about this, if this should be necessary. Do you see a third alternative? Jakob.scholbach (talk) 16:39, 28 March 2011 (UTC)
 * I think it's fine as is, now. Randomblue (talk) 02:20, 29 March 2011 (UTC)
 * Could a more thorough explanation fit in a note? A. Parrot (talk) 17:17, 28 March 2011 (UTC)

--- end of paste Jakob.scholbach (talk) 16:03, 28 March 2011 (UTC) ---
 * "Typical handheld calculators calculate the logarithms to bases 10 and e." -> Citation needed. Also, as a suggestion, maybe put a picture illustrate this. Randomblue (talk) 02:20, 29 March 2011 (UTC)
 * Why do you want a citation for that? Do you consider this a debated statement? (If not, isn't WP:BLUE applying here?). About the picture: previously we had complaints that the article contained too many pictures. Since a photo of a calculator is not something really new to many readers, I prefer not to add a picture to illustrate this. Jakob.scholbach (talk) 17:21, 29 March 2011 (UTC)
 * I want a citation since I got the only two "handheld calculators" I own (which even do square roots) but neither has a log or ln function. The statement seems OR to me, that's all. Randomblue (talk) 02:52, 30 March 2011 (UTC)
 * It should probably say "handheld scientific calculator", per definition a scientific caluculator is one that can perform standard mathematical operations such as ln or log, in addition to basic arithmetic.TR 12:33, 30 March 2011 (UTC)
 * Citation given. Jakob.scholbach (talk) 19:28, 31 March 2011 (UTC)

Comments from Cryptic C62

 * No mention of Euler in the lead? This makes me sad.
 * Thanks for your comments. Sorry about making you sad, though! I think Euler's contribution to logarithm might be paraphrased by polishing a concept which was widespread before him. (He was able to do so because he pushed analysis a good deal further.) This is reflected by the short mention that we give him (which in turn is based on the similarly short mention of his contribution to this topic in the literature, see one of the posts above). Once we accept this, we must reflect this in the lead, which is why he does not appear in the lead section. Less sad now? Jakob.scholbach (talk) 17:02, 23 April 2011 (UTC)
 * Yes, less sad now. As long as exclusion of topics from the lead was a conscious choice backed up by sound reasoning, then I'm fine with it; I was just checking to make sure that the topics in question hadn't been forgotten about. --Cryptic C62 · Talk 00:35, 24 April 2011 (UTC)


 * "Since adding is an easier manual computation than multiplying, scientists, engineers and others rapidly adopted logarithms for calculations after John Napier invented them in the early 17th century." What did Napier invent? Assuming this refers to logarithms themselves, I suggest splitting this important historical fact into its own sentence, preferably before the manual computation bit.
 * I'll think more about this, but currently I don't see why this sentence could be ambiguous: the only other thing Napier could have invented from a grammatical point of view (with the current wording) would be "scientists, engineers, and others", clearly absurd.
 * About the phrasing: I find the current wording quite nice and smooth: we start out with what is most important: the product formula. We relate this to history (log tables and slide rules), go on to further motivate their historical importance. The fact that it was Napier who invented them is, admittedly, important, but less important than the fact that logs were used a lot in science etc. (After all, Bürgi also came up with the idea. Maybe the time was just ripe for them to be invented?) I'm happy to consider other suggestions, but right now I would not want to change it the way you are sketching. Jakob.scholbach (talk) 17:02, 23 April 2011 (UTC)


 * "For example, the decibel is a logarithmic unit quantifying sound pressure and voltage ratios. Moreover, the Richter scale quantifies the seismic energy produced by earthquakes." The word "moreover" wrongly implies that the second sentence is an elaboration upon the first. Perhaps "similarly" would be a better choice.
 * OK. Jakob.scholbach (talk) 17:02, 23 April 2011 (UTC)
 * "The logarithm of a product is the sum of the logarithms of the factors:" This sentence and the formula that follows it are good to have in the lead, but I'm concerned that readers may be mislead into thinking that this is the only useful property of logarithms. The absence of logarithmic differentiation from the lead is also a bit puzzling, as this is a very useful technique for dealing with complicated functions. It may be possible to brutally murder both of these birds with a single stone: something like "Several other properties of logarithms also yield useful formulas; the ease with which logarithms can be manipulated gives rise to such techniques as logarithmic differentiation". It's not perfect, but perhaps you'll be able to come up with a good alternative.
 * It is not the only, but (by a huge margin) the most important property of logarithms. We have to give this importance to this formula. On the other hand, I don't share (or at least don't understand) your concern that the reader might believe it is the only important thing.
 * Secondly, I don't consider logarithmic differentiation to be this important. As far as I understand, it is mostly a trick to calculate derivatives, but not an essential piece of mathematics. Again, we have to match the lead section with the article structure. The article mentions this quite briefly (rightfully, IMO). By implication, the lead section should not overemphasize this. Jakob.scholbach (talk) 17:02, 23 April 2011 (UTC)
 * See my first response above. --Cryptic C62 · Talk 00:35, 24 April 2011 (UTC)


 * "Joost Bürgi independently discovered logarithms but published four years after Napier." Discovery and invention are interchangeable. Why does the article insist that Napier invented logs but that Burgi discovered them?
 * Changed to "invented". Jakob.scholbach (talk) 17:02, 23 April 2011 (UTC)
 * "Euler also established the modern definition for logarithms." Which is...? This sentence teases the reader and leaves him wanting more.
 * Tweaked. Jakob.scholbach (talk) 17:02, 23 April 2011 (UTC)
 * "This approach yields high precision approximations of the natural logarithm." Which approach? This phrasing assumes that the reader will be able to correctly interpret the name of the section name. This is unlikely to be the case for non-mathematicians.
 * Alright. Jakob.scholbach (talk) 17:02, 23 April 2011 (UTC)
 * "Entropy is broadly a measure of the (dis-)order of some system." This is a very amateurish pseudoword construction. I strongly suggest replacing "(dis-)order" with have "disorder".
 * OK. Jakob.scholbach (talk) 17:33, 24 April 2011 (UTC)


 * In the Music subsection, there is a series of equalities, but they are only approximations. I suggest replacing each instance of = with \approx.
 * OK. Jakob.scholbach (talk) 17:33, 24 April 2011 (UTC)


 * "This property is captured by a Lyapunov exponent being positive." I have never heard of a property being captured, nor can I safely say that I understand what this bizarre phrase is trying to convey.
 * Reworded. Jakob.scholbach (talk) 20:40, 26 April 2011 (UTC)


 * In the majority of cases, the article uses "log(n)" or "ln(3)" or whatever. There are a handful of instances of "log n" and "ln 3". These need to be made consistent.
 * I did try to convert all log 3 etc. into log(3) recently. What did I miss? Thanks. Jakob.scholbach (talk) 20:40, 26 April 2011 (UTC)
 * There are some at the end of Power series, in the main formula of Arithmetic-geometric mean approximation, in the text of Entropy and chaos, the last formula of Number theory, and the last formula of Complex logarithm.
 * Oh, I forgot to watch out for the ln's. Now fixed. Jakob.scholbach (talk) 18:40, 28 April 2011 (UTC)


 * In the Complex logarithm section, the word "not" is italicized for emphasis. If I had a team of monkeys working for me, I would have them scamper through the MOS to try to find a relevant policy regarding such emphasis. I have no such team. I will instead use my intuition, which tells me that italicization in this manner is unencyclopedic and ambiguous in meaning. If the reader can't figure out how to read and process each word in a sentence without having to scan through it for emphasized words, they should just get off the planet.
 * I guess I'm the monkey now: WP:MOS says "Italics may be used sparingly to emphasize words in sentences" (the emphasis is original, ironically). So we are on the safe side here. This failure of the identities for complex logarithms is really a key point, so emphasizing it is OK. This is the only emphasis in italics we have in the whole article. Jakob.scholbach (talk) 20:40, 26 April 2011 (UTC)
 * Well I'll be a monkey's uncle! This is one of the rare instances in which the MOS and I disagree. Struck. --Cryptic C62 · Talk 23:56, 27 April 2011 (UTC)


 * "The graph at the right depicts Log(z)." Phrases like this make me very sad, particularly when I read them on my iPad and can't figure out what graph is being referred to.
 * Maybe tell Apple your problem? It is this. Do you see a way of making it more plain than it is now? The image caption of that picture is clearly connected to the sentence you are quoting by their common mention of "Log(z)". Jakob.scholbach (talk) 20:40, 26 April 2011 (UTC)
 * The point I was trying to make is that article text should try to avoid referring to graphics or other sections whenever possible, as we really have no way of predicting how well the phrases will translate to mobile/offline/mirror services. I realize that I may be alone in this preference, so I'm not going to push the issue. --Cryptic C62 · Talk 23:56, 27 April 2011 (UTC)
 * Hm. I think removing the reference would be unhelpful to most readers (i.e., those with a reasonable rendering) and I understand it is common practice to have the reference. Some editors include things such as "Figure 1" etc., but I think this clutters up the whole appearance. Jakob.scholbach (talk) 18:40, 28 April 2011 (UTC)


 * "The discrete logarithm is concerned with solving the equation" People can be concerned. Cats can sometimes be concerned. Logarithms are never concerned. They are laid back and inanimate. I suggest replacing this with "the discrete logarithm is used to solve the equation" or some such.
 * Reworded. Jakob.scholbach (talk) 14:26, 30 April 2011 (UTC)

Summary
Images checked (pls ping Nikkimaria for confirmation that all is in order and images haven't changed), reliability of sources checked (pls ping Brianboulton for same, unless Fifelfoo covered that), it is not clear that a close paraphrasing spot check has been done. There is a statement from an IP that an oppose still stands and it will revisit, their time is up and we don't know who the IP is. Have opposers revisted recently?
 * Update: Nikkimaria has raised a couple of image concerns. Sandy Georgia  (Talk) 15:35, 30 May 2011 (UTC)
 * I've responded to his concerns. Jakob.scholbach (talk) 18:34, 30 May 2011 (UTC)
 * Hers. Nikkimaria (talk) 19:44, 30 May 2011 (UTC)
 * Sorry! Jakob.scholbach (talk) 19:15, 31 May 2011 (UTC)


 * Support
 * 1)  on 2c
 * 1)  on 2c
 * 1)  on 2c
 * 1)  on 2c
 * 1)  on 2c
 * 1)  on 2c
 * 1)  on 2c
 * 1)  on 2c
 * 1)  on 2c

[Removed opposition; see the page itself; sorry, I was away from WP when contacted about this. N oetica Tea? 00:42, 30 May 2011 (UTC)]
 * Oppose


 * Unclear or not stated
 * , neutral (<--added by Jakob.scholbach (talk))
 * , neutral, oppose struck,
 * , significant contributor
 * , clarified neutral but no problems
 * Note, it would not be considered canvassing to post a neutrally worded request to these editors to revisit to enter a declaration. Sandy Georgia  (Talk) 14:05, 29 May 2011 (UTC)
 * Note, it would not be considered canvassing to post a neutrally worded request to these editors to revisit to enter a declaration. Sandy Georgia  (Talk) 14:05, 29 May 2011 (UTC)
 * Note, it would not be considered canvassing to post a neutrally worded request to these editors to revisit to enter a declaration. Sandy Georgia  (Talk) 14:05, 29 May 2011 (UTC)
 * Note, it would not be considered canvassing to post a neutrally worded request to these editors to revisit to enter a declaration. Sandy Georgia  (Talk) 14:05, 29 May 2011 (UTC)
 * Note, it would not be considered canvassing to post a neutrally worded request to these editors to revisit to enter a declaration. Sandy Georgia  (Talk) 14:05, 29 May 2011 (UTC)


 * Unactionable


 * Image review
 * OK

Has been asked to visit? Sandy Georgia (Talk) 13:49, 29 May 2011 (UTC)
 * I see he has; followup. Sandy Georgia  (Talk) 13:58, 29 May 2011 (UTC)
 * Response:  Sandy Georgia  (Talk) 23:00, 29 May 2011 (UTC)


 * I just flooded a number of user talk pages: I pinged Nikkimaria and Brianboulton and asked them to update their review and/or strike out their comments, if they are covered. I also asked NuclearWarfare, Pichpich, Lightmouse, David Eppstin and ManfromButtonwillow whether they want to declare either "support" or "oppose". (I did not ask Dicklyon, since I consider him an essential contributor to the article. Moreover, I did not ask GrahamColm, since he explicitly said that he can just remove his earlier "Oppose" and replace it by a non-declaration, i.e., doesn't feel like supporting it, but also does not hold up his oppose.) Jakob.scholbach (talk) 15:23, 29 May 2011 (UTC)
 * None of the three editors explicitly opposing the nomination (Randomblue, Tony1, Noetica) have responded to my request to update their concerns (which I posted on May 6th and May 10th, respectively). Jakob.scholbach (talk) 15:23, 29 May 2011 (UTC)
 * Should Dicklyon be added as a co-nominator? Sandy Georgia  (Talk) 16:02, 29 May 2011 (UTC)
 * This is necessarily subjective, but I consider myself as the main driving editor both for the basic development of the article and also for carrying it to and through FAC. Therefore, I did not ask Dicklyon or anyone else to be co-nom. (My comment above was just to indicate that I consider Dick to be involved in the article, and hence asking for support or oppose for the nomination seemed to run agains the guideline that only uninvolved editors should judge.) Jakob.scholbach (talk) 16:52, 29 May 2011 (UTC)
 * It's a question of whether you believe his/her contributions should be recognized at WP:WBFAN should the article be promoted (or alternately, per FAC rules, be prohibited from nominating another FAC within two weeks, should the article be archived)-- at his/her contrib level, s/he could also add themself. Sandy Georgia  (Talk) 17:02, 29 May 2011 (UTC)
 * OK, I see. No, I don't think Dick should be a co-nominator. (He never expressed any intention of being co-nom, for example here would have been an occasion to do so.) Jakob.scholbach (talk) 17:16, 29 May 2011 (UTC)
 * NuclearWarfare said he/she is not going to either support or oppose this nomination. Jakob.scholbach (talk) 16:52, 29 May 2011 (UTC)
 * Oh, I forgot to say: I did not ping Pmanderson now, since I already did so a few weeks ago. Jakob.scholbach (talk) 16:52, 29 May 2011 (UTC)

Congratulations to the promotion, Jakob. At long last. :) Nageh (talk) 08:53, 2 June 2011 (UTC)
 * Merci! Jakob.scholbach (talk) 12:38, 2 June 2011 (UTC)