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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.
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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
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I have to nominate "Numbers are placed on slide rule scales at a distance proportional to their common logarithm. By mechanically adding the distance for 1 to 2 on the lower scale to the distance from 1 to 3 on the upper scale, one can quickly determine that 2 x 3 = 6." for funniest
Serious Caption
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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
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was a prodigious mental calculator. Reputedly, when asked how he had been able to predict the trajectory of Ceres with such accuracy he replied, "I used logarithms." The questioner then wanted to know how he had been able to look up so many numbers from the tables so quickly. "Look them up?" Gauss
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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
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I have a rather old book with a "Table of
Mantissas" in the back and I was wondering if perhaps someone could either explain more on how to use such a table in the article, or explain how to use mine in this discussion page. Mine has a table of numbers down the side, beginning with 10 and ending
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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"?
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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.
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logarithm. Why is that? It is because all multiplicative powers of 10 as stated earlier in the article are derived from any logarithm by simply counting the number of positions of the most significant digit from the decimal point to ascertain the value of the
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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.
375:= 10: decfrac = decfrac + partial X = X / 10 partial = partial / 10 X=X*X*X*X*X*X*X*X*X*X return (integer_value + decfrac) if __name__ == '__main__': value = 4.5 print " X =",value print "LOG10(X) =",log10(value)
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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.
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The primary importance, however, is the demonstration that the identification of mantissa and characteristic is not an archaic or obsolete exercise given the modern convenience of automated computations of the logarithm function.
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1.52, rounded to four digits, is 0.1818. Then suppose you want the base-10 logarithm of 1520, which is the number that results from starting with 1.52 and pushing the decimal point three places to the right. That logarithm is
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Even though this article is short on sourcing, adding new unstuffed stuff like the big section on use in plotting, complete with pseudocode, is not acceptable. If we can verify that this technique is indeed used, via a
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Suppose you want the base-10 logarithm of 1.52. You look at "15" (the first two digits) in the left-marginal column, then find "2" (the third digit) in the top margin, then look at the entry: 1818. Conclude that
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showing the derivation of the mantissa and characteristic of a number given its base 10 logarithm. The derivations are given by the second line of headings below each of the headings annotating the chart.
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1520 = 3.1818 (approximately). The "3" is how many places the decimal point was pushed; that's why using 10 as the base of logarithms is convenient when working in a base-10 numeral system. 3 is the
1841:"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."
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The use of logarithms is an elementary and standard technique used for generating scales in many graphing environments. It is a fundamental technique that is ubiquitous in the computing industry.
372:#!/usr/bin/python from __future__ import division def log10(X): epsilon = 0.000000000001 integer_value=0 while X < 1: integer_value = integer_value - 1 X = X * 10 while X : -->
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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.
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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.
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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.
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mantissa several times and if one wishes to think of it as a table of logarithms, then it is a table of only a single entry - that of 5 - so it is a table of
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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
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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.
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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.
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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.
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got a calculator and can get the base-10 logarithm without doing that, then what's the point? The article should communicate the idea.
373:= 10: integer_value = integer_value + 1 X = X / 10 decfrac = 0.0 partial = 1/10 X=X*X*X*X*X*X*X*X*X*X while partial : -->
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of logarithms will have a single indexed entry for the same mantissa. In the example, 0.698 970 (004 336 018 ...) will be listed
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My old mathematics teacher at school also led me to believe that while ln is a standard abbreviation of log
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with 99 going by 1s. The top has numbers from 0 through 9 going by 1s also. As such, it looks like this:
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CAN SOMEONE PLEASE PUT UP SIMPLE INSTRUCTIONS ON HOW YOU WORK OUT THE LOG10 OF A NUMBER THANK YOU
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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The "Uses" section doesn't actually mention any uses. There should certainly be several.
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If it's standard, it shouldn't be hard to find a source and make it verifiable, yes?
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Not that anyone gives a damn but here is an algorithm for calculating log10(x)
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help? Maybe there should be a mention here to look at the explanation there.
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The logarithm is the inverse operation of exponentiation and obeys four laws:
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wrote it as a sentence, with "gave", in the orignal lead in 2003, but then
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Common
Logarithm, Characteristic and Mantissa of Powers of 10 for a Number
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Should this article discuss who invented Common logarithms? I think it was
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a few years later. And nobody noticed until now. Aren't we all flaky?
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946:{\displaystyle 2)~~log_{a}\left({x \over y}\right)~=~log_{a}x~-~log_{a}y}
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x. If ISO really says log10 it's not much of an ambiguity mitigation.
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Anyway, I was just kind of hoping someone could explain it to me...
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to calculators. i'd love to see this issue fleshed out a bit.
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And he has restored it to "gave" after I poked him about it.
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1160:{\displaystyle 4)~~log_{a}x~=~log_{a}y~~if~and~only~if~x=y}
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Yes, in computer science lg generally denotes log base 2.
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Note that the mantissa is common to all of the 5×10i. A
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1212:Thanks. The link wasn't highlighted before.--
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606:{\displaystyle If~x=a^{y},~~then,~y=log_{a}x}
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301:logarithm#Easier computations
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120:and see a list of open tasks.
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1930:121.7.54.103
1927:
1861:— Preceding
1856:
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1696:.698 970...
1676:.698 970...
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1214:Charlesrkiss
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721:0~and~y: -->
714:0~and~y: -->
626:0~and~y: -->
618:
615:
513:
512:to the base
509:
502:
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496:Introduction
473:
469:
455:
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382:
368:
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323:Henry Briggs
320:
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305:Gene Nygaard
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176:CyborgTosser
172:
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51:WikiProjects
34:
1754:—Preceding
1742:thus lists
1579:(= 5 × 10)
1536:as per the
1288:—Preceding
1234:—Preceding
722:0,}" /: -->
506:mathematics
476:—Preceding
430:Gauss Quote
350:—Preceding
280:explanation
123:Mathematics
114:mathematics
70:Mathematics
1966:Categories
1886:mangled it
1718:lists the
1681:0.000 005
1610:5 000 000
1528:- it is a
1472:0.000 005
1416:5 000 000
317:Originator
271:Thank you.
1850:Bold text
1584:floor(log
1566:mantissa
1392:floor(log
1193:logarithm
1189:logarithm
627:0,}": -->
421:Hilarious
39:is rated
1924:Question
1908:Dicklyon
1890:Dicklyon
1863:unsigned
1756:unsigned
1736:mantissa
1336:Dicklyon
1313:Dicklyon
1290:unsigned
1267:Dicklyon
1248:contribs
1236:unsigned
478:unsigned
352:unsigned
333:contribs
247:mantissa
169:Untitled
1818:"Uses"?
1549:number
1363:number
150:on the
41:C-class
1943:Naming
1857:showed
458:Shahab
330:(talk)
47:scale.
1716:chart
1705:table
1538:chart
1530:chart
1349:Table
1263:WP:RS
1197:Bkell
702:: -->
680:: -->
441:Gauss
28:This
1954:talk
1934:talk
1912:talk
1894:talk
1871:talk
1828:talk
1809:talk
1790:lg x
1780:talk
1764:talk
1744:only
1734:the
1720:same
1714:The
1709:once
1661:0.5
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1317:talk
1298:talk
1271:talk
1244:talk
1218:talk
1201:talk
1176:talk
486:talk
360:talk
327:maru
325:. --
142:High
1748:are
1732:but
1687:−6
1667:−1
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1595:log
1592:))
1552:log
1478:−6
1464:−1
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1403:log
1400:))
1372:log
715:0,}
504:In
249:.
237:log
232:log
221:99
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1936:)
1914:)
1896:)
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1852::
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1766:)
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1436:1
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1405:10
1394:10
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1319:)
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1250:)
1246:•
1220:)
1203:)
1178:)
1170:--
920:−
662:∈
488:)
453:.
447:”
437:“
389:10
362:)
295:)
239:10
234:10
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1932:(
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1149:x
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1122:d
1119:n
1116:a
1111:f
1108:i
1101:y
1096:a
1092:g
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1085:l
1080:=
1075:x
1070:a
1066:g
1062:o
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1052:)
1049:4
1026:x
1021:a
1017:g
1013:o
1010:l
1007:n
1002:=
995:n
991:x
985:a
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936:a
932:g
928:o
925:l
915:x
910:a
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894:=
888:)
883:y
880:x
875:(
869:a
865:g
861:o
858:l
851:)
848:2
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816:g
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804:+
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770:y
767:x
764:(
759:a
755:g
751:o
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738:1
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683:0
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670:,
666:R
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654:,
651:x
646:,
643:n
638:r
635:o
632:F
601:x
596:a
592:g
588:o
585:l
582:=
579:y
574:,
571:n
568:e
565:h
562:t
555:,
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546:a
542:=
539:x
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518:a
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385:e
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154:.
53::
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