1433:
829:
133:
1428:{\displaystyle {\begin{array}{rll}{\text{As found above,}}&\log _{10}(0.012)\approx {\bar {2}}.07918\\{\text{Since}}\;\;\log _{10}(0.85)&=\log _{10}\left(10^{-1}\times 8.5\right)=-1+\log _{10}(8.5)&\approx -1+0.92942={\bar {1}}.92942\\\log _{10}(0.012\times 0.85)&=\log _{10}(0.012)+\log _{10}(0.85)&\approx {\bar {2}}.07918+{\bar {1}}.92942\\&=(-2+0.07918)+(-1+0.92942)&=-(2+1)+(0.07918+0.92942)\\&=-3+1.00860&=-2+0.00860\;^{*}\\&\approx \log _{10}\left(10^{-2}\right)+\log _{10}(1.02)&=\log _{10}(0.01\times 1.02)\\&=\log _{10}(0.0102).\end{array}}}
270:
1877:
36:
1991:
3034:. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications.
603:
608:
To avoid the need for separate tables to convert positive and negative logarithms back to their original numbers, one can express a negative logarithm as a negative integer characteristic plus a positive mantissa. To facilitate this, a special notation, called
451:
The last number (0.07918)—the fractional part or the mantissa of the common logarithm of 120—can be found in the table shown. The location of the decimal point in 120 tells us that the integer part of the common logarithm of 120, the characteristic, is 2.
1973:
for the natural logarithm. Today, both notations are found. Since hand-held electronic calculators are designed by engineers rather than mathematicians, it became customary that they follow engineers' notation. So the notation, according to which one writes
1793:
446:
309:
An important property of base-10 logarithms, which makes them so useful in calculations, is that the logarithm of numbers greater than 1 that differ by a factor of a power of 10 all have the same fractional part. The fractional part is known as the
1884:
scales at distances proportional to the differences between their logarithms. By mechanically adding the distance from 1 to 2 on the lower scale to the distance from 1 to 3 on the upper scale, one can quickly determine that
321:, can be computed by simply counting how many places the decimal point must be moved, so that it is just to the right of the first significant digit. For example, the logarithm of 120 is given by the following calculation:
2284:
2188:
683:
1924:) logarithms, in order to suggest a change to Napier's logarithms. During these conferences, the alteration proposed by Briggs was agreed upon; and after his return from his second visit, he published the first
289:. By turning multiplication and division to addition and subtraction, use of logarithms avoided laborious and error-prone paper-and-pencil multiplications and divisions. Because logarithms were so useful,
2092:
815:
2517:
2433:
314:. Thus, log tables need only show the fractional part. Tables of common logarithms typically listed the mantissa, to four or five decimal places or more, of each number in a range, e.g. 1000 to 9999.
466:
1649:
1982:" when the natural logarithm is intended, may have been further popularized by the very invention that made the use of "common logarithms" far less common, electronic calculators.
2802:
327:
2759:
2694:
2726:
751:
1839:
715:
273:
Page from a table of common logarithms. This page shows the logarithms for numbers from 1000 to 1509 to five decimal places. The complete table covers values up to 9999.
2314:
1859:
1641:
688:
The bar over the characteristic indicates that it is negative, while the mantissa remains positive. When reading a number in bar notation out loud, the symbol
2193:
2097:
2006:) on a typical scientific calculator. The advent of hand-held calculators largely eliminated the use of common logarithms as an aid to computation.
285:
of base-10 logarithms were used in science, engineering and navigation—when calculations required greater accuracy than could be achieved with a
3109:
3084:
3039:
293:
of base-10 logarithms were given in appendices of many textbooks. Mathematical and navigation handbooks included tables of the logarithms of
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2865:
3003:
119:
53:
2016:
759:
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2354:
100:
72:
57:
598:{\displaystyle \log _{10}(0.012)=\log _{10}\left(10^{-2}\times 1.2\right)=-2+\log _{10}(1.2)\approx -2+0.07918=-1.92082.}
1909:
165:
79:
820:
with the actual value of the result of a calculation determined by knowledge of the reasonable range of the result.
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is read as "bar 2 point 07918...". An alternative convention is to express the logarithm modulo 10, in which case
220:(logarithm with base e ≈ 2.71828) rather than common logarithm when writing "log". To mitigate this ambiguity, the
1788:{\displaystyle \log _{10}\left(x\times 10^{i}\right)=\log _{10}(x)+\log _{10}\left(10^{i}\right)=\log _{10}(x)+i.}
86:
2594:
stems from an older, non-numerical, meaning: a minor addition or supplement, e.g., to a text. Nowadays, the word
1445:
The following table shows how the same mantissa can be used for a range of numbers differing by powers of ten:
68:
46:
1873:, 0.698 970 (004 336 018 ...) will be listed once indexed by 5 (or 0.5, or 500, etc.).
441:{\displaystyle \log _{10}(120)=\log _{10}\left(10^{2}\times 1.2\right)=2+\log _{10}(1.2)\approx 2+0.07918.}
2835:
2829:
294:
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1903:
278:
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2667:
2010:
The numerical value for logarithm to the base 10 can be calculated with the following identities:
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724:
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2908:
Institutionum
Analyticarum Pars Secunda de Calculo Infinitesimali Liber Secundus de Calculo Integrali
2639:
3128:
2620:(1825). "Über die Berechnung der geographischen Längen und Breiten aus geodätischen Vermessungen".
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1805:
269:
2879:
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2629:
290:
282:
1931:
Because base-10 logarithms were most useful for computations, engineers generally simply wrote "
691:
2828:
Hall, Arthur Graham; Frink, Fred
Goodrich (1909). "Chapter IV. Logarithms Common logarithms".
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2319:
217:
93:
3095:
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2330:
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132:
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The following example uses the bar notation to calculate 0.012 × 0.85 = 0.0102:
834:
3025:
2871:
1876:
281:
capable of multiplication were bulky, expensive and not widely available. Instead,
17:
3031:
Handbook of
Mathematical Functions with Formulas, Graphs, and Mathematical Tables
2906:
2603:
2553:
2533:
1913:
1621:
277:
Before the early 1970s, handheld electronic calculators were not available, and
221:
141:
35:
2279:{\displaystyle \quad \log _{10}(x)={\frac {\log _{B}(x)}{\log _{B}(10)}}\quad }
2183:{\displaystyle \quad \log _{10}(x)={\frac {\log _{2}(x)}{\log _{2}(10)}}\quad }
1912:, a 17th century British mathematician. In 1616 and 1617, Briggs visited
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1449:
Common logarithm, characteristic, and mantissa of powers of 10 times a number
286:
213:
2651:
3101:
1990:
1917:
1862:
298:
149:
3094:
Poliyanin, Andrei
Dmitrievich; Manzhirov, Alexander Vladimirovich (2007) .
1908:
Common logarithms are sometimes also called "Briggsian logarithms" after
2538:
1925:
1439:
2911:(in Latin). Vol. 2. Joannis Thomæ Nob. De Trattnern. p. 198.
1447:
678:{\displaystyle \log _{10}(0.012)\approx {\bar {2}}+0.07918=-1.92082.}
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is ambiguous, as this can also mean the complex natural logarithmic
460:
Positive numbers less than 1 have negative logarithms. For example,
2762:
2634:
1989:
131:
3049:
1865:
to include only one entry for each mantissa. In the example of
29:
2087:{\displaystyle \log _{10}(x)={\frac {\ln(x)}{\ln(10)}}\quad }
810:{\displaystyle \log _{10}(0.012)\approx 8.07918{\bmod {1}}0,}
792:
168:, an English mathematician who pioneered its use, as well as
2512:{\displaystyle {d \over dx}\log _{10}(x)={1 \over x\ln(10)}}
2318:
as procedures exist for determining the numerical value for
1438:* This step makes the mantissa between 0 and 1, so that its
2804:, the eccentricity of the earth ellipsoid (a small number).
2428:{\displaystyle {d \over dx}\log _{b}(x)={1 \over x\ln(b)}}
216:, it is printed as "log", but mathematicians usually mean
136:
A graph of the common logarithm of numbers from 0.1 to 100
3076:
Engineering
Acoustics: An Introduction to Noise Control
2598:
is generally used to describe the fractional part of a
2771:
2734:
2702:
2670:
2441:
2357:
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2196:
2100:
2019:
1847:
1808:
1652:
1629:
832:
762:
727:
694:
622:
469:
330:
3097:
Handbook of mathematics for engineers and scientists
2602:
number on computers, though the recommended term is
1920:, the inventor of what are now called natural (base-
60:. Unsourced material may be challenged and removed.
2834:. Vol. Part I: Plane Trigonometry. New York:
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1612:Note that the mantissa is common to all of the
2327:Natural logarithm § Efficient computation
2761:, the minor radius of the earth ellipsoid in
297:as well. For the history of such tables, see
8:
2867:Introductio in Analysin Infinitorum (Part 2)
1951:. Mathematicians, on the other hand, wrote "
2823:
2821:
2728:. From the context, it is understood that
2345:The derivative of a logarithm with a base
2335:Algorithms for computing binary logarithms
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120:Learn how and when to remove this message
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2289:using logarithms of any available base
1802:is a constant, the mantissa comes from
2996:"Derivatives of Logarithmic Functions"
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152:with base 10. It is also known as the
7:
2977:Logarithmic and Trigonometric Tables
2944:
2942:
58:adding citations to reliable sources
2797:{\displaystyle e=10^{8.9054355-10}}
25:
2754:{\displaystyle b=10^{6.51335464}}
2689:{\displaystyle \log b=6.51335464}
3006:from the original on 2020-10-01.
2721:{\displaystyle \log e=8.9054355}
746:{\displaystyle {\bar {2}}.07918}
172:. Historically, it was known as
34:
2974:Hedrick, Earle Raymond (1913).
2664:gives (beginning of section 8)
2556:(also commonly called mantissa)
2275:
2197:
2179:
2101:
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45:needs additional citations for
2856:; du Pasquier, Louis Gustave;
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1841:, which is constant for given
1828:
1822:
1773:
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1714:
1708:
1620:. This holds for any positive
1415:
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1024:
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989:
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782:
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568:
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489:
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423:
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350:
344:
1:
2905:Scherffer, P. Carolo (1772).
2870:. 1 (in Latin). Vol. 9.
1834:{\displaystyle \log _{10}(x)}
317:The integer part, called the
2923:"Introduction to Logarithms"
305:Mantissa and characteristic
160:, named after its base, or
3145:
2765:(a large number), whereas
1901:
710:{\displaystyle {\bar {n}}}
3079:. Springer. p. 448.
2622:Astronomische Nachrichten
2860:; Trost, Ernst (1945) .
2652:10.1002/asna.18260041601
3073:Möser, Michael (2009).
1442:(10) can be looked up.
295:trigonometric functions
222:ISO 80000 specification
2836:Henry Holt and Company
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279:mechanical calculators
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137:
2955:mathworld.wolfram.com
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2590:This use of the word
2579:multi-valued function
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2430:
2311:
2309:{\displaystyle \,B~.}
2281:
2185:
2089:
1993:
1904:History of logarithms
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272:
180:. It is indicated by
174:logarithmus decimalis
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27:Mathematical function
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2017:
1994:The logarithm keys (
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1806:
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54:improve this article
2949:Weisstein, Eric W.
2644:1825AN......4..241B
2549:Napierian logarithm
1928:of his logarithms.
1863:table of logarithms
1450:
456:Negative logarithms
178:logarithmus decadis
162:Briggsian logarithm
18:Logarithmus decadis
3022:Abramowitz, Milton
2951:"Common Logarithm"
2927:www.mathsisfun.com
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2008:
1959:" when they meant
1939:" when they meant
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1448:
1425:
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807:
743:
707:
675:
595:
438:
275:
236:should be written
170:standard logarithm
138:
69:"Common logarithm"
3111:978-1-58488-502-3
3086:978-3-540-92722-8
3041:978-0-486-61272-0
3026:Stegun, Irene Ann
2980:. New York, USA:
2544:Logarithmic scale
2507:
2455:
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2302:
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2177:
2081:
1854:{\displaystyle x}
1636:{\displaystyle x}
1622:real number
1610:
1609:
1149:
1131:
1027:
891:
878:
840:
737:
704:
657:
218:natural logarithm
158:decimal logarithm
154:decadic logarithm
130:
129:
122:
104:
16:(Redirected from
3136:
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3069:
3028:, eds. (1983) .
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2862:Speiser, Andreas
2858:Brandt, Heinrich
2854:Speiser, Andreas
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2582:
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2571:
2529:Binary logarithm
2518:
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2515:
2510:
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2506:
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2399:
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2331:logarithm base 2
2323:
2315:
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2300:
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2272:
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2110:
2093:
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2090:
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2063:
2046:
2029:
2028:
2005:
2001:
1998:for base-10 and
1981:
1972:
1958:
1950:
1938:
1892:
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1872:
1870:
1861:. This allows a
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146:common logarithm
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2850:Euler, Leonhard
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2320:logarithm base
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1460:Characteristic
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839:As found above,
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723:
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718:
690:
689:
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617:
549:
513:
512:
508:
495:
470:
465:
464:
458:
404:
374:
373:
369:
356:
331:
326:
325:
307:
259:
251:
245:
237:
229:
225:
209:
208:with a capital
201:
200:, or sometimes
193:
189:
181:
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
3142:
3140:
3132:
3131:
3121:
3120:
3117:
3116:
3110:
3091:
3085:
3070:
3040:
3016:
3013:
3010:
3009:
3002:. 2021-04-14.
2987:
2966:
2938:
2914:
2897:
2841:
2816:
2815:
2813:
2810:
2807:
2806:
2791:
2788:
2785:
2781:
2777:
2774:
2748:
2744:
2740:
2737:
2717:
2714:
2711:
2708:
2705:
2685:
2682:
2679:
2676:
2673:
2628:(8): 852–861.
2608:
2600:floating-point
2583:
2565:
2564:
2562:
2559:
2558:
2557:
2551:
2546:
2541:
2536:
2531:
2524:
2521:
2505:
2502:
2499:
2496:
2493:
2490:
2486:
2481:
2478:
2475:
2472:
2469:
2464:
2460:
2453:
2450:
2446:
2421:
2418:
2415:
2412:
2409:
2406:
2402:
2397:
2394:
2391:
2388:
2385:
2380:
2376:
2369:
2366:
2362:
2349:is such that
2342:
2339:
2305:
2299:
2287:
2286:
2271:
2268:
2265:
2262:
2257:
2253:
2247:
2244:
2241:
2238:
2233:
2229:
2222:
2219:
2216:
2213:
2210:
2205:
2201:
2175:
2172:
2169:
2166:
2161:
2157:
2151:
2148:
2145:
2142:
2137:
2133:
2126:
2123:
2120:
2117:
2114:
2109:
2105:
2079:
2076:
2073:
2070:
2067:
2062:
2059:
2056:
2053:
2050:
2044:
2041:
2038:
2035:
2032:
2027:
2023:
1987:
1984:
1962:
1942:
1902:Main article:
1899:
1896:
1850:
1830:
1827:
1824:
1821:
1816:
1812:
1796:
1795:
1784:
1781:
1778:
1775:
1772:
1769:
1766:
1761:
1757:
1753:
1749:
1744:
1740:
1736:
1732:
1727:
1723:
1719:
1716:
1713:
1710:
1707:
1702:
1698:
1694:
1690:
1684:
1680:
1676:
1673:
1669:
1665:
1660:
1656:
1632:
1608:
1607:
1601:
1598:
1595:
1594:−5.301 029...
1592:
1588:
1587:
1581:
1578:
1575:
1574:−0.301 029...
1572:
1568:
1567:
1564:
1561:
1558:
1555:
1551:
1550:
1547:
1544:
1541:
1538:
1534:
1533:
1530:
1527:
1524:
1521:
1517:
1516:
1514:
1503:
1500:
1492:
1486:
1478:
1475:
1468:
1467:
1466:Combined form
1464:
1461:
1458:
1455:
1436:
1435:
1420:
1417:
1414:
1411:
1408:
1403:
1399:
1395:
1392:
1390:
1387:
1384:
1381:
1378:
1375:
1372:
1367:
1363:
1359:
1356:
1354:
1351:
1348:
1345:
1340:
1336:
1332:
1328:
1323:
1320:
1316:
1312:
1308:
1303:
1299:
1295:
1292:
1290:
1285:
1279:
1276:
1273:
1270:
1267:
1264:
1262:
1259:
1256:
1253:
1250:
1247:
1245:
1242:
1239:
1236:
1233:
1230:
1227:
1224:
1221:
1218:
1215:
1212:
1209:
1206:
1203:
1201:
1198:
1195:
1192:
1189:
1186:
1183:
1180:
1177:
1174:
1171:
1168:
1165:
1162:
1159:
1157:
1154:
1148:
1145:
1139:
1136:
1130:
1127:
1121:
1118:
1116:
1113:
1110:
1107:
1102:
1098:
1094:
1091:
1088:
1085:
1082:
1077:
1073:
1069:
1066:
1064:
1061:
1058:
1055:
1052:
1049:
1044:
1040:
1036:
1035:
1032:
1026:
1023:
1017:
1014:
1011:
1008:
1005:
1002:
999:
997:
994:
991:
988:
983:
979:
975:
972:
969:
966:
962:
958:
955:
950:
947:
943:
938:
934:
929:
925:
921:
918:
916:
913:
910:
907:
902:
898:
887:
886:
883:
877:
874:
868:
865:
862:
859:
856:
851:
847:
843:
836:
835:
818:
817:
806:
803:
798:
794:
790:
787:
784:
781:
778:
775:
770:
766:
742:
736:
733:
703:
700:
686:
685:
674:
671:
668:
665:
662:
656:
653:
647:
644:
641:
638:
635:
630:
626:
606:
605:
594:
591:
588:
585:
582:
579:
576:
573:
570:
567:
564:
561:
556:
552:
548:
545:
542:
539:
535:
531:
528:
523:
520:
516:
511:
507:
502:
498:
494:
491:
488:
485:
482:
477:
473:
457:
454:
449:
448:
437:
434:
431:
428:
425:
422:
419:
416:
411:
407:
403:
400:
397:
393:
389:
386:
381:
377:
372:
368:
363:
359:
355:
352:
349:
346:
343:
338:
334:
319:characteristic
306:
303:
247:
227:
191:
128:
127:
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3141:
3130:
3127:
3126:
3124:
3113:
3107:
3104:. p. 9.
3103:
3099:
3098:
3092:
3088:
3082:
3078:
3077:
3071:
3067:
3063:
3059:
3055:
3051:
3047:
3043:
3037:
3033:
3032:
3027:
3023:
3019:
3018:
3014:
3005:
3001:
2997:
2991:
2988:
2983:
2979:
2978:
2970:
2967:
2956:
2952:
2945:
2943:
2939:
2928:
2924:
2918:
2915:
2910:
2909:
2901:
2898:
2893:
2881:
2873:
2869:
2868:
2863:
2859:
2855:
2851:
2845:
2842:
2838:. p. 31.
2837:
2833:
2832:
2824:
2822:
2818:
2811:
2789:
2786:
2783:
2779:
2775:
2772:
2764:
2746:
2742:
2738:
2735:
2715:
2712:
2709:
2706:
2703:
2683:
2680:
2677:
2674:
2671:
2661:
2657:
2653:
2649:
2645:
2641:
2636:
2631:
2627:
2623:
2619:
2618:Bessel, F. W.
2615:For example,
2612:
2609:
2605:
2601:
2597:
2593:
2587:
2584:
2580:
2573:The notation
2570:
2567:
2560:
2555:
2552:
2550:
2547:
2545:
2542:
2540:
2537:
2535:
2532:
2530:
2527:
2526:
2522:
2520:
2500:
2494:
2491:
2488:
2484:
2479:
2473:
2467:
2462:
2458:
2451:
2448:
2444:
2416:
2410:
2407:
2404:
2400:
2395:
2389:
2383:
2378:
2374:
2367:
2364:
2360:
2350:
2348:
2340:
2338:
2336:
2332:
2328:
2324:
2316:
2303:
2297:
2266:
2260:
2255:
2251:
2242:
2236:
2231:
2227:
2220:
2214:
2208:
2203:
2199:
2170:
2164:
2159:
2155:
2146:
2140:
2135:
2131:
2124:
2118:
2112:
2107:
2103:
2074:
2068:
2065:
2057:
2051:
2048:
2042:
2036:
2030:
2025:
2021:
2013:
2012:
2011:
1997:
1992:
1986:Numeric value
1985:
1983:
1979:
1970:
1965:
1956:
1948:
1936:
1929:
1927:
1923:
1919:
1915:
1911:
1905:
1897:
1883:
1878:
1874:
1864:
1848:
1825:
1819:
1814:
1810:
1782:
1779:
1776:
1770:
1764:
1759:
1755:
1751:
1747:
1742:
1738:
1734:
1730:
1725:
1721:
1717:
1711:
1705:
1700:
1696:
1692:
1688:
1682:
1678:
1674:
1671:
1667:
1663:
1658:
1654:
1646:
1645:
1644:
1630:
1623:
1602:
1600:0.698 970...
1599:
1596:
1593:
1590:
1589:
1582:
1580:0.698 970...
1579:
1576:
1573:
1570:
1569:
1566:0.698 970...
1565:
1563:0.698 970...
1562:
1559:
1557:0.698 970...
1556:
1553:
1552:
1549:1.698 970...
1548:
1546:0.698 970...
1545:
1542:
1540:1.698 970...
1539:
1536:
1535:
1532:6.698 970...
1531:
1529:0.698 970...
1528:
1525:
1523:6.698 970...
1522:
1519:
1518:
1515:
1513:
1509:
1501:
1498:
1490:
1487:
1484:
1476:
1473:
1470:
1469:
1465:
1462:
1459:
1456:
1453:
1452:
1446:
1443:
1441:
1418:
1412:
1406:
1401:
1397:
1393:
1382:
1379:
1376:
1370:
1365:
1361:
1357:
1349:
1343:
1338:
1334:
1330:
1326:
1321:
1318:
1314:
1310:
1306:
1301:
1297:
1293:
1283:
1277:
1274:
1271:
1268:
1265:
1260:
1257:
1254:
1251:
1248:
1237:
1234:
1231:
1225:
1219:
1216:
1213:
1207:
1204:
1196:
1193:
1190:
1187:
1181:
1175:
1172:
1169:
1166:
1160:
1152:
1143:
1137:
1134:
1125:
1119:
1111:
1105:
1100:
1096:
1092:
1086:
1080:
1075:
1071:
1067:
1059:
1056:
1053:
1047:
1042:
1038:
1030:
1021:
1015:
1012:
1009:
1006:
1003:
1000:
992:
986:
981:
977:
973:
970:
967:
964:
960:
956:
953:
948:
945:
941:
936:
932:
927:
923:
919:
911:
905:
900:
896:
881:
872:
866:
860:
854:
849:
845:
826:
825:
824:
821:
804:
801:
796:
788:
785:
779:
773:
768:
764:
756:
755:
754:
740:
731:
698:
672:
669:
666:
663:
660:
651:
645:
639:
633:
628:
624:
616:
615:
614:
612:
611:bar notation,
592:
589:
586:
583:
580:
577:
574:
571:
565:
559:
554:
550:
546:
543:
540:
537:
533:
529:
526:
521:
518:
514:
509:
505:
500:
496:
492:
486:
480:
475:
471:
463:
462:
461:
455:
453:
435:
432:
429:
426:
420:
414:
409:
405:
401:
398:
395:
391:
387:
384:
379:
375:
370:
366:
361:
357:
353:
347:
341:
336:
332:
324:
323:
322:
320:
315:
313:
304:
302:
300:
296:
292:
288:
284:
280:
271:
267:
263:
255:
250:
241:
233:
223:
219:
215:
205:
197:
185:
179:
175:
171:
167:
163:
159:
155:
151:
147:
143:
134:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
3096:
3075:
3030:
3015:Bibliography
2999:
2990:
2976:
2969:
2958:. Retrieved
2954:
2930:. Retrieved
2926:
2917:
2907:
2900:
2872:B.G. Teubner
2866:
2844:
2831:Trigonometry
2830:
2625:
2621:
2611:
2595:
2591:
2586:
2569:
2351:
2346:
2344:
2317:
2288:
2009:
1995:
1977:
1968:
1963:
1954:
1946:
1934:
1930:
1921:
1910:Henry Briggs
1907:
1797:
1611:
1606:.698 970...
1586:.698 970...
1511:
1507:
1496:
1488:
1482:
1471:
1444:
1437:
822:
819:
687:
610:
607:
459:
450:
318:
316:
311:
308:
276:
261:
253:
248:
239:
231:
203:
195:
183:
177:
173:
169:
166:Henry Briggs
161:
157:
153:
145:
139:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
2888:|work=
2604:significand
2554:Significand
2534:Cologarithm
1914:John Napier
1491:= floor(log
721:", so that
214:calculators
156:and as the
142:mathematics
110:August 2020
3129:Logarithms
2960:2020-08-29
2932:2020-08-29
2812:References
2747:6.51335464
2684:6.51335464
2341:Derivative
1882:slide rule
1591:0.000 005
1520:5 000 000
1457:Logarithm
287:slide rule
258:should be
80:newspapers
3102:CRC Press
2982:Macmillan
2890:ignored (
2880:cite book
2787:−
2784:8.9054355
2716:8.9054355
2707:
2675:
2660:118630614
2635:0908.1823
2495:
2468:
2411:
2384:
2261:
2237:
2209:
2165:
2141:
2113:
2069:
2052:
2031:
2002:for base-
1918:Edinburgh
1820:
1765:
1731:
1706:
1675:×
1664:
1474:= 5 × 10
1463:Mantissa
1407:
1380:×
1371:
1344:
1319:−
1307:
1294:≈
1284:∗
1269:−
1252:−
1208:−
1188:−
1167:−
1147:¯
1129:¯
1120:≈
1106:
1081:
1057:×
1048:
1025:¯
1004:−
1001:≈
987:
968:−
954:×
946:−
933:
906:
876:¯
867:≈
855:
786:≈
774:
735:¯
702:¯
670:−
655:¯
646:≈
634:
613:is used:
590:−
575:−
572:≈
560:
541:−
527:×
519:−
506:
481:
427:≈
415:
385:×
367:
342:
299:log table
150:logarithm
3123:Category
3066:65-12253
3050:64-60036
3004:Archived
2596:mantissa
2592:mantissa
2523:See also
1643:because
673:1.92082.
593:1.92082.
436:0.07918.
312:mantissa
164:, after
3058:0167642
2864:(ed.).
2640:Bibcode
2539:Decibel
1926:chiliad
1898:History
1454:Number
1440:antilog
1278:0.00860
1261:1.00860
1238:0.92942
1232:0.07918
1197:0.92942
1176:0.07918
1013:0.92942
789:8.07918
664:0.07918
584:0.07918
148:is the
94:scholar
3108:
3083:
3064:
3056:
3048:
3038:
3000:Math24
2658:
2329:) and
2301:
1798:Since
1413:0.0102
1153:.92942
1135:.07918
1031:.92942
882:.07918
741:.07918
291:tables
283:tables
244:, and
144:, the
96:
89:
82:
75:
67:
2763:toise
2656:S2CID
2630:arXiv
2561:Notes
2435:, so
2333:(see
2325:(see
1891:3 = 6
1087:0.012
1054:0.012
890:Since
861:0.012
780:0.012
640:0.012
487:0.012
212:; on
101:JSTOR
87:books
3106:ISBN
3081:ISBN
3062:LCCN
3046:LCCN
3036:ISBN
2892:help
2190:or
2094:or
1953:log(
1933:log(
1571:0.5
1510:) −
1383:1.02
1377:0.01
1350:1.02
1112:0.85
1060:0.85
912:0.85
202:Log(
182:log(
73:news
2704:log
2672:log
2648:doi
2626:331
2575:Log
2459:log
2375:log
2337:).
2252:log
2228:log
2200:log
2156:log
2132:log
2104:log
2022:log
1996:log
1976:ln(
1961:log
1941:log
1916:at
1811:log
1756:log
1722:log
1697:log
1655:log
1597:−6
1577:−1
1537:50
1502:log
1499:))
1477:log
1398:log
1362:log
1335:log
1298:log
1097:log
1072:log
1039:log
993:8.5
978:log
957:8.5
924:log
897:log
846:log
793:mod
765:log
625:log
566:1.2
551:log
530:1.2
497:log
472:log
421:1.2
406:log
388:1.2
358:log
348:120
333:log
260:ln(
246:log
238:lg(
226:log
190:log
176:or
140:In
56:by
3125::
3100:.
3060:.
3054:MR
3052:.
3044:.
3024:;
2998:.
2953:.
2941:^
2925:.
2884::
2882:}}
2878:{{
2852:;
2820:^
2790:10
2780:10
2743:10
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