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result. Physics will just say F = m a, where the variables keep the units. The former might result in excess conversions, the latter unusual units. Since computer languages normally don't keep units in variables, the engineering way is convenient for programming. And, as with the question here, units go out before the logs.
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No, please do not make excellently accessible featured articles less friendly to novice readers without consensus, and please don't engage in edit warring. The explanation is not "redundant", and the line you call "*identical*" is self evidently different. Please look again more carefully, and try to
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I think all of your proposals are less clear or helpful for the lead section of this article than the existing text. Conflating "logarithm" and "logarithm function" is common and not really a serious problem. The distinction could be mentioned somewhere in a footnote or later down the article but I
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This is vaguely on the topic of the last discussion. I note that the article doesn't really properly define logarithms. The section on the definition is a standard one used in pre-calculus, but it is not suitable for analysis, which uses properties of the natural logarithm instead. Thus, really
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Reminds me that it seems to me that engineers often write expressions and equations with units factored out, while physicists keep units in. That is, one might say F(Newtons) = m (kg) * a (m/s/s). The expectation is that one converts to the given units, applies the formula, and then converts the
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From the integral definition of the natural log, "the area under the curve of a plot of 1/x versus x", it is clear that x can have any unit and that the logarithm is always unitless. The "area" under the curve has units of the x-axis times the units of the y-axis which, in all cases, is unity and
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There are some discussion on the web suggestion things like "you can't take the logarithm of a number with units" (which is absurd, scientists and engineers do it all the time), to basically "there is a hidden and highly secret process in which the units disappear". Like "actually log(x*unit) is
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The fact that the logarithm removes the units means that taking a logarithm is a lossy transform. There is no way, other than external knowledge, that allows the unit to be recovered by taking the exponent of the log. Therefore, e^(Ln(x)) <:
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I have edited the beginning of the lead for avoiding the ambiguous (here) "exponentiation", using a formulation proposed above by
Jacobolus (I read Jacobolus' formulation only after having edited the lead).
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To be clear, inverse functions are defined for univariate functions only, and exponentiation is a bivariate function. So, for having an inverse function, one must fix one variable (
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Really need a section on the units of a logarithm. For example, what is the unit of Log(10/seconds)? That is a common expression in first order rate equations, like nuclear decay.
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rather than considering a family of single-variable exponential functions but that does not have a well-defined inverse as it is not even locally 1-1 from its inputs (the pair
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That is a useful property of the logarithm function, but it does not describe what the function is. I don't see what's wrong with the current lead. Each exponential function
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If you want to be precise, the logarithm function is the inverse of the exponential function (or a logarithm function is the inverse of an exponential function). The term
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Engineer here - Just because we often do things like take the logarithm of numbers with units does not mean we should. For example, expanding something like
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Following Lazard (25 July 2024) we can conclude that the first sentence of the lede is wrong - since 2015. The definition shouldn't speak of the inverse
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I made the text a bit more explicit. Does that help? (As always, anyone should feel free to keep working on this who thinks they can improve on it.) –
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I believe is interesting since I have never seen before the approximation for splitting the logarith of a sum before finding it accidentally here {
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Jacobolus surprisingly reverted an edit that removed a verbatim copy of a line two lines above that line. I'm re-reverting it after with him.
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includes both power function and exponential function. The important difference, and I don't know which one you are asking about, is between
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presuming knowledge of the not very elementary (IMHO) bivariate operation ^ for real variables, instead of addition and multiplication.
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when it transforms multiplication into addition: f(uv) = f(u) + f(v) . Or - in an indirect way - when it is the inverse function of an
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1) Euler's exponentials and inversion, the standard approach since 1748. This is a circular definition since exponentials are also
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Taking this in a weird direction, it means that we can make equivalence relations between log units in some weird ways. Consider
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I think it could be interesting to add an approximation for splitting the logarithm of a sum which rises from approximating the
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We can "pretend" the units are dimensionless because we plan to just call the units of the solution something like
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proved in 1933 that every locally compact group has an invariant measure, as mentioned in the list of examples at
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This seems excessively pedantic and confusing, but it's plausible we could make up a better first few paragraphs.
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make sense. I don't know what to do with a result like this, but it does serve your point that clearly one
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ln(seconds) == (ln(meters) - ln(acceleration))/2 == ln( (m / (m/s^2)) ^ (1/2) ) == ln( (seconds^2) ^ (1/2))
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is defined as an integral (or in some other equivalent way). The problem with the definition "The real
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base b of y" really needs a mysterious rewriting of an equation? There really isn't a more direct way?
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take logarithms of units when we define them -- Otherwise, I would personally consider something like
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with just a change of variables it will lead to how approximate splitting the sum of a logarithm as:
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that really helps a lot! Thank you for spending time on this, and sorry for the confrontation.
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Yes, I agree. Particularly since the definition given in the article already isn't "wrong"
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Explaining this is fine, but it should be done below the first half of this article. –
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think belaboring it at the start is distracting. Anything involving symbols such as
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is also routinely applied to the logarithm function, or to an expression such as
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take the logarithm of a number with units. In fact, one can use a logarithm of
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The argument in question winds up being dimensionless by cancellation.
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of St-Vincent and de Sarasa was used from 1647 to 1748; it relies on
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Please can you motivate why (an - improved? - variant of Aug 24):
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Isn't root extraction also an inverse function of exponentiation?
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You could also define a different two-variable powering function
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An alternative would be to say something like: "In the equation
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really log(x*unit/1*unit) so the units cancel", which is wrong.
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is more helpful to provide context here for most readers than
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Is the definition only precise, using the inverse function?:
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Why "the quantity b, x, y" ? This letters are used here as
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ln(acceleration) == ln(m/s^2) == ln(meters) - 2*ln(seconds)
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Featured articles that have appeared on the main page once
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f(u+v) = f(u) · f(v) for all pairs u, v of pos. numbers."
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which leads to the following smooth approximation to the
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Is this simple and clear enough to start the lead with?
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does not belong in the lead section of this article. –
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is a (written) expression with a symbol for a certain
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put yourself in the shoes of a non-technical reader. –
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1628:exponentiation
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784:exponentiation
776:exponentiation
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768:power function
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1377:
1353:
1343:
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1291:
1273:
1263:
1245:
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1212:the quantity
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1191:
1187:
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1148:
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1120:
1116:
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928:
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841:
837:
833:
829:
825:
824:
823:
819:
815:
803:
799:
798:
797:
793:
789:
785:
781:
777:
773:
770:redirects to
769:
765:
762:Well, first,
761:
759:
758:
757:
753:
749:
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741:
739:
738:
737:
736:
732:
728:
714:
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631:
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623:
619:
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611:
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584:
583:
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556:
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531:
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510:
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479:
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367:
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353:
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336:
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157:
149:
145:
141:
137:
133:
129:
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120:
119:
111:
110:Verifiability
108:
106:
103:
101:
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52:Learn to edit
49:
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2748:
2535:
2300:0,\ x\neq y}
2249:page): with
2236:
2073:
2034:
2012:— Preceding
2001:
1989:Haar measure
1982:
1978:signed areas
1971:
1956:
1953:
1934:
1899:
1709:
1673:
1546:
1542:
1536:
1530:
1521:
1515:0 ≠1, x: -->
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1507:
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1341:
1289:
1261:
972:
968:
885:
881:
877:
851:
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839:
835:
827:
724:
705:MüllerMarcus
665:MüllerMarcus
662:
621:
617:
613:
609:
605:
596:
586:
579:
575:
571:ln(x) -: -->
570:
566:
562:
558:
554:
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534:
515:
511:
507:
504:
497:
478:Top-priority
477:
437:
403:Top‑priority
381:WikiProjects
364:
334:
321:
316:June 1, 2011
302:
283:
264:
214:please do so
203:
195:
155:
121:
94:
19:This is the
1985:Alfréd Haar
1939:Tito Omburo
1904:Tito Omburo
852:exponential
848:logarithmic
597:log-seconds
535:log(x*unit)
453:Mathematics
444:mathematics
400:Mathematics
304:Peer review
31:not a forum
2772:Categories
2306:0,\ y: -->
2299:0,\ y: -->
2253:0,\ y: -->
2078:function:
1797:such that
1710:defined as
1498:) iff
1392:, denoted
509:unitless.
271:Not listed
205:identified
2243:LogSumExp
1919:jacobolus
1636:jacobolus
1601:jacobolus
1537:logarithm
1531:variables
1525:Jacobolus
1437:jacobolus
1342:logarithm
957:jacobolus
886:logarithm
878:logarithm
836:logarithm
812:th root.
693:jacobolus
681:jacobolus
369:is rated
196:Logarithm
88:if needed
71:Be polite
25:Logarithm
21:talk page
2076:Softplus
2026:contribs
2014:unsigned
1751:, where
1652:D.Lazard
1614:D.Lazard
1262:exponent
882:exponent
855:0, ≠1) .
828:function
814:D.Lazard
748:D.Lazard
612:, which
599:anyways.
371:FA-class
328:Promoted
309:Reviewed
156:365 days
123:Archives
56:get help
29:This is
27:article.
2239:maximum
2041:Rgdboer
2018:Rgdboer
1972:2) The
1900:natural
1559:Hesselp
1551:Hesselp
981:Hesselp
861:Hesselp
480:on the
249:Process
1935:per se
1290:result
774:, and
520:Jsluka
377:scale.
290:Listed
252:Result
2276:: -->
2262:: -->
1516:0 ."
1344:base
537:into
358:This
198:is a
84:Seek
2760:talk
2060:talk
2045:talk
2022:talk
1943:talk
1908:talk
1656:talk
1618:talk
1563:talk
1555:talk
1510:(or
1494:(or
1480:(or
1167:talk
985:talk
971:(or
865:talk
818:talk
792:talk
788:Gah4
782:and
752:talk
731:talk
709:talk
669:talk
647:talk
643:Gah4
630:talk
614:does
524:talk
246:Date
73:and
2320:max
1983:3)
1922:(t)
1865:exp
1708:is
1684:log
1639:(t)
1634:. –
1604:(t)
1440:(t)
1409:log
1368:of
1054:log
1002:exp
960:(t)
955:. –
929:log
918:or
696:(t)
684:(t)
618:can
578:or
567:can
557:or
545:to
517:-->
472:Top
2774::
2762:)
2717:
2714:ln
2701:−
2685:
2682:ln
2654:
2651:ln
2627:
2624:ln
2621:−
2605:
2602:ln
2578:
2575:ln
2568:≈
2550:
2547:ln
2504:
2501:ln
2488:−
2472:
2469:ln
2441:
2438:ln
2420:−
2404:
2401:ln
2379:≈
2347:
2344:ln
2341:≈
2290:≠
2212:≠
2193:
2190:ln
2179:−
2171:−
2135:
2132:ln
2121:≈
2092:
2089:ln
2062:)
2047:)
2039:—
2028:)
2024:•
2010:.
1999:.
1969:.
1945:)
1910:)
1880:
1877:ln
1868:
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1693:
1658:)
1620:)
1565:)
1549:.
1545:/
1418:
1316:,
1169:)
1063:
1011:
987:)
967:A
938:
901:
898:ln
867:)
820:)
794:)
786:.
754:)
733:)
711:)
671:)
649:)
632:)
526:)
154::
146:,
142:,
138:,
134:,
130:,
54:;
2758:(
2726:)
2723:2
2720:(
2710:1
2705:y
2694:)
2691:2
2688:(
2678:1
2673:x
2663:)
2660:2
2657:(
2647:1
2642:y
2636:)
2633:y
2630:(
2614:)
2611:2
2608:(
2598:1
2593:x
2587:)
2584:x
2581:(
2565:)
2562:y
2559:+
2556:x
2553:(
2513:)
2510:2
2507:(
2497:y
2492:e
2481:)
2478:2
2475:(
2465:x
2460:e
2450:)
2447:2
2444:(
2434:y
2429:e
2423:y
2413:)
2410:2
2407:(
2397:x
2392:e
2386:x
2376:)
2371:y
2367:e
2363:+
2358:x
2354:e
2350:(
2338:}
2335:y
2330:,
2327:x
2324:{
2293:y
2287:x
2282:,
2279:0
2273:y
2268:,
2265:0
2259:x
2215:0
2209:x
2204:,
2196:2
2186:/
2182:x
2175:e
2168:1
2164:x
2155:,
2152:0
2149:=
2146:x
2141:,
2138:2
2126:{
2117:)
2111:x
2107:e
2103:+
2100:1
2096:(
2058:(
2043:(
2020:(
1963:b
1941:(
1906:(
1886:)
1883:b
1874:y
1871:(
1843:y
1839:b
1818:x
1815:=
1810:y
1806:b
1785:y
1765:x
1739:x
1729:/
1725:b
1696:x
1688:b
1654:(
1616:(
1597:
1584:R
1575:
1561:(
1553:(
1527::
1523:@
1472::
1468:@
1433:
1421:y
1413:b
1405:=
1402:x
1394:
1390:
1378:y
1370:
1366:
1354:b
1346:
1338:
1326:x
1318:
1314:
1302:x
1294:
1286:
1274:y
1266:
1258:
1246:x
1238:
1234:
1222:b
1214:
1210:
1196:x
1192:b
1188:=
1185:y
1177:
1165:(
1149:y
1146:,
1143:x
1121:y
1117:x
1113:=
1110:)
1107:y
1104:,
1101:x
1098:(
1095:f
1072:)
1069:x
1066:(
1058:b
1031:x
1027:b
1023:=
1020:)
1017:x
1014:(
1006:b
983:(
953:
941:a
933:b
920:
916:
904:x
890:
863:(
816:(
810:n
806:n
790:(
750:(
729:(
707:(
667:(
645:(
628:(
580:C
576:R
563:x
559:C
555:R
551:R
543:x
522:(
484:.
383:.
216:.
148:6
144:5
140:4
136:3
132:2
128:1
125::
58:.
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