Talk:Common logarithm

message: Has anyone else heard of the approximation at the end of the article?  My dad said they used to use it back in college when calculators didn't do logarithms.  It would be interesting to know how far back it dates, and how long, if ever, it was in common use. CyborgTosser 09:55, 17 May 2004 (UTC)
thread_title: Untitled

message: i like this article, but i got directed to it due to interest in why the calculator made base-10 logs obsolete.  unfortunately, this article really doesn't address that question.
for example, it states, "Because of their utility in saving work in laborious calculations by hand on paper, tables of base-10 logarithms were found in appendices of many books."  as a non-mathematician, i have no idea why base-10 logs "save work..."  and therefore i can't understand the connection to calculators.  i'd love to see this issue fleshed out a bit.
s (unsigned by User:24.89.202.141)
:Does the explanation at logarithm#Easier computations help?  Maybe there should be a mention here to look at the explanation there.  Gene Nygaard 19:11, 10 October 2005 (UTC)
thread_title:  explanation 

message: Should this article discuss who invented Common logarithms? I think it was Henry Briggs. --maru  (talk) contribs 16:35, 26 January 2006 (UTC)
thread_title:  Originator 

message: Not that anyone gives a damn but here is an algorithm for calculating log10(x)
Does anyone know who invented this algorithm?  —Preceding unsigned comment added by 130.75.46.195 (talk) 14:16, 20 December 2007 (UTC)
thread_title:  Algorithm for log10(x) 

message: My old mathematics teacher at school also led me to believe that while ln is a standard abbreviation of loge, lg was an accepted abbreviation of log10. Has anyone else seen lg used?
:I've seen it, but if I came across it without some context, I would be uncertain which base was intended.  I suspect some people use lg for the base-2 logarithm. Michael Hardy 21:52, 24 May 2006 (UTC)
replies: text: Yes, in computer science lg generally denotes log base 2. —Steven G. Johnson 04:03, 25 May 2006 (UTC)
thread_title:  Further notation 

message: .
Can be put in the article.--Shahab 19:39, 22 June 2007 (UTC)
thread_title: Gauss Quote

message: I've just changed the approximation formula which contained a mistake. Repeatedly taking the square root eleven times is equivalent to raising to the power 1/2048, not 1/2047 as given in the formula. The factor 889 is roughly 2048/log(10) (which is actually 889.4). Curiously, 2047/log(10) is very nearly 889 (it's 889.001) but this is mere coincidence. I presume it has something to do with why the original author had given 2047 instead of 2048 in the first place though. The main source error is the approximation for the logarithm of a number close to 1 (i.e. log x = x - 1). Using 889 instead of 889.435... will make the approximation worse for all numbers less than 1 and some greater than 1 but after a certain point, it will counter the effect of the log x = x - 1 approximation. That's certainly not a good reason to use 889 specifically though: you could say the same about using 1000 or 3551. The only reason to use 889 instead of 889.435... is that it's easier to remember and might be accurate enough for the users needs.
After all that, although it's an interesting calculator trick I don't think it should be included in the article unless someone can reference it.  —Preceding unsigned comment added by 86.153.11.148 (talk) 01:08, 4 November 2007 (UTC)
thread_title:  The approximation 

message: Let's have the most useful information first, please.  I'm not too familiar with line spacing in this Wiki; it would be nice to even things out a little bit: lowering "4)", for example. Thanks.
In mathematics, the logarithm of x to the base a is written as logax  and is defined by the statement:
:If~ x=a^y, ~~then, ~y=log_{a}x 
The logarithm is the inverse operation of exponentiation and obeys four laws:
: For ~n,~ x,~ y \in \mathbb{R}, ~~x>0 ~and~ y>0,
:1)~~log_{a}(xy)~=~log_{a}x~+~log_{a}y 
:2)~~log_{a}\left({x \over y}\right)~=~log_{a}x~-~log_{a}y 
:3)~~log_{a}x^n~=~nlog_{a}x 
:4)~~log_{a}x~=~log_{a}y~~  if~and~only~if~ x=y 
--Charlesrkiss (talk) 04:56, 23 February 2008 (UTC)
replies: text: That information should be in the logarithm article, not in the introduction here, since it's not specific to the common logarithm. If a reader is uncertain what a logarithm is, he or she can click the logarithm link in the first sentence of this article. —Bkell (talk) 06:31, 23 February 2008 (UTC)
thread_title:  Introduction 

message: Is this in any way helpful to the article?  Does it have a reliable source, or just the wiki?  I expect I'll remove that as well as the bit on plotting that is being thrashed around, unless someone shows a source where they can be verified and explain whey they're useful.  Dicklyon (talk) 16:08, 22 October 2009 (UTC)
thread_title:  What's with the Python code? 

message: I changed the table to read as follows:
: 
number   	mantissa (from the table)	characteristic 	log10(n)
n        	                         	floor(log10(n))	log10(n) − characteristic
5 000 000	0.698970004336018...     	  6       	  6.698970004336018...
50       	0.698970004336018...     	  1       	  1.698970004336018...
5        	0.698970004336018...     	  0       	  0.698970004336018...
0.5      	0.698970004336018...     	−1             	−0.301029995663981...
0.000 005	0.698970004336018...     	−6             	−5.301029995663981...
: 
It does not make sense to put the base-10 logarithm column first.  That's against the whole spirit of this concept.  The reason base 10 is used is that you can get the mantissa out of the table and then use a bit of common sense to find the characteristic and hence the base 10 logarithm.  If you've got a calculator and can get the base-10 logarithm without doing that, then what's the point?  The article should communicate the idea.  Michael Hardy (talk) 17:55, 26 October 2009 (UTC)
replies: text: (Oh, and by the way, whoever recently arranged the table to show them in a different order used a hyphen instead of a minus sign.) Michael Hardy (talk) 17:56, 26 October 2009 (UTC)

text: I understand that this is not a table of logarithms, but I think a table of logarithms would better serve the puprposes of this article. Michael Hardy (talk) 18:52, 11 November 2009 (UTC)
thread_title:  Table 

message: "To mitigate this ambiguity the ISO specification is that log10(x) should be lg (x)."
Whaaaat????  I always thought lg x was log2 x.  If ISO really says log10 it's not much of an ambiguity mitigation.
66.127.55.192 (talk) 10:09, 17 February 2010 (UTC)
thread_title:  lg x 

message: The "Uses" section doesn't actually mention any uses.   There should certainly be several. Michael Hardy (talk) 21:44, 19 February 2010 (UTC)
thread_title:  "Uses"? 

message: "Such a table of "common logarithms" giving the logarithm, often to 4 or 5 decimal places, of each number in the left-hand column, which ran from 1 to 10 by small increments, perhaps 0.01 or 0.001."
That's not a sentence, and I don't understand the article's topic enough to fix it. I understand English grammar and syntax quite well, but I don't understand math or this article's topic well enough to correct the problems in the sentence.
Here's my best guess, with my suggested change in Bold text:
Such a table of "common logarithms" showed the logarithm, often to 4 or 5 decimal places, of each number in the left-hand column, which ran from 1 to 10 by small increments, perhaps 0.01 or 0.001.  — Preceding unsigned comment added by 131.96.118.157 (talk) 22:01, 8 July 2011 (UTC)
replies: text: User:Michael Hardy wrote it as a sentence, with "gave", in the orignal lead in 2003, but then mangled it a few years later.  And nobody noticed until now.  Aren't we all flaky?  Dicklyon (talk) 03:05, 9 July 2011 (UTC)
replies: text: And he has restored it to "gave" after I poked him about it.  Dicklyon (talk) 19:54, 9 July 2011 (UTC)
thread_title:  Sentence fragment makes meaning unclear 

message: Is log(x) = 10x? 121.7.54.103 (talk) 09:47, 2 May 2013 (UTC)
thread_title: Question

message: The article gives a list of variously obscure names -- I just encountered "decadic" somewhere, and wanted to check it was the obvious meaning -- but surely it is vastly more common to call it a "logarithm base 10", or "base 10 logarithm", than any form other than "common"? Imaginatorium (talk) 05:07, 18 February 2016 (UTC)
thread_title:  Naming