Maths
Numbers - Log Table

How to find the logarithm of a number, using four figure log tables (below)
To find the log of a number, you first need the two parts of the answer - the index or characteristic (the part before the decimal point) and the mantissa (the decimal part after the decimal point). For example, the index of 2.6742 is 2 and the mantissa is .6742.
 
Finding the index of a logarithm
This is easy if you follow these rules:
For numbers with more than 1 digit before the decimal point (10 and above), the index will always be one less than the number of digits before the decimal point. For example, the index of 245.211 is 2, the index of 24521.1 is 4 and the index of 24.5211 is 1.
For numbers with just 1 digit before the decimal point (1 to 9), the index will be 0. For numbers less than 1, then index will be one more than the number of zeros between the decimal point and the first significant figure. For example, the index of 0.245211 is (bar) 1, the index of 0.00245211 is (bar) 3 and the index of 0.000245211 is (bar) 4.
 
Finding the mantissa of a logarithm
Use the numbers at the far left of the table to give the first two significant figures of the number. If there are more than two digits in the number, follow across the table - the column headings give the third digit of the number. The numbers given in the log table represent the mantissa part of the answer.
For Example:
To find log 45, follow down the numbers on the far left of the table until you reach 45. The number in the column headed 0 will be the mantissa - the index is 1 (see above) - so log 45 = 1.6532.
To find log 456, follow down the numbers on the far left of the table until you reach 45 and take the number in column 6. The index is 2, so log 456 = 2.6590.
 
Using the Mean Difference Column for numbers with four digits
For numbers with four digits, simply add the number in the mean difference column (right hand 9 columns) to the answer you would get if you just ignored the fourth digit.
For Example:
To find log 4567, take the log of 456 (2.6590) and add the number in column 7 of the mean differences (7) to the mantissa. ie. log 4567 = 3.6590 + 0.0007 = 3.6597.
 
Finding logs of numbers smaller than one
This is simple - just find the log of the four significant figures of the number, and and take away the index.
For Example:
To find the log of 0.004567, take log 4.567 = 0.6597 and subtract 3 (the index). So log 0.004567 = (log 4.567) - 3 = -2.3403.

 
N0123456789123456789
1000000043008601280170 5 9 13172126303438
021202530294033403744 8 12162024283236
1104140453049205310569 4 8 12162023273135
060706450682071907554 7 11151822262933
1207920828086408990934 3 7 11141821252832
096910041038107211063 7 10141720242731
1311391173120612391271 3 6 10131619232629
130313351367139914303 7 10131619222529
1414611492152315531584 3 6 9 121519222528
161416441673170317323 6 9 121417202326
1517611790181818471875 3 6 9 111417202326
190319311959198720143 6 8 111417192225
1620412068209521222148 3 6 8 111416192224
217522012227225322793 5 8 101316182123
1723042330235523802405 3 5 8 101315182023
243024552480250425293 5 8 101215172022
1825532577260126252648 2 5 7 9 1214171921
267226952718274227652 4 7 9 1114161821
1927882810283328562878 2 4 7 9 1113161820
290029232945296729892 4 6 8 1113151719
N0123456789123456789
20301030323054307530963118313931603181320124681113151719
21322232433263328433043324334533653385340424681012141618
22342434443464348335023522354135603579359824681012141517
2336173636365536743692371137293747376637842467911131517
2438023820383838563874389239093927394539622457911121416
2539793997401440314048406540824099411641332357910121415
2641504166418342004216423242494265428142982357810111315
274314433043464362437843934409442544404456235689 111314
284472448745024518453345484564457945944609235689 111214
294624463946544669468346984713472847424757134679 101213
N0123456789123456789
304771478648004814482948434857487148864900134679101113
314914492849244955496949834997501150245038134678101112
32505150655079509251055119513251455159517213457891112
33518551985211522452375250526352765289530213456891012
34531553285340535353665378539154035416542813456891011
35544154535465547854905502551455275539555112456791011
36556355755587559956115623563556475658567012456781011
3756825694570557175729574057525763577557861235678910
3857985809582158235843585558665877588858991235678910
3959115922593359445955596659775988599960101235678910
N0123456789123456789
4060216031604260536064607560856069610761171234568910
416128613861496160617061806191620162126222123456789
426232624362536263627462846294630463146235123456789
436335634563556365637563856395640564156425123456789
446435644464546464647464846493650365136522123456789
456532654265516561657165806590659966096618123456789
466628663766466656666566756684669367026712123456778
476721673067396749675867676776678567946803123455678
486812682168306839684868576866687568846893123445678
496902691169206928693769466955690469726981123445678
N0123456789123456789
50699069987007701670247033704270507059706712345678
51707670847093710171107118712671357143715212345678
52716071687177718571937202721072187226723512245677
53724372517259726772757284729273007308731612245667
54732473327340734873567364737273807388739612245667
557404741274197427743574437451745974667474122345567
567482749074977505751375207528753675457551122345567
577559756675747582758975977604761276197627122345567
587634764276497657766476727679768676947701112344567
597709771677237731773877457752776077677774112344567
N0123456789123456789
607782778977967803781078187825783278397846112344566
617853786078687875788278897896790379107917112344566
627924793179387945795279597966797379807987112334566
637993800080078014802180288035804180488055112334556
648062806980758082808980968102810981168122112334556
658129813681428149815681628169817681828189112334556
668195820282098215822282288235824182488254112334556
678261826782748280828782938299830683128319112334556
688325833183388344835183578363837083768382112334456
698388839584018407841484208426843284398445112234456
N0123456789123456789
708451845784638470847684828488849485008506112234456
718513851985258531853785438549855585618567112234455
728573857985858591859786038609861586218627112234455
738633863986458651865786638669867586818686112234455
748692869897048710871687228727873387398745112234455
758751875687628768877487798785879187978802112233455
768808881488208825883188378842884888548859112233455
778865887188768882888788938899890489108915112233445
788921892789328938894389498954896089658971112233445
798976898289878993899890049009901590209025112233445
N0123456789123456789
809031903690429047905390589063906990749079112233445
819085909090969101910691129117912291289133112233445
829138914391499154915991659170917591809186112233445
839191919692019206921292179222922792329238112233445
849243924892539258926392699274927992849289112233445
859249929993049309931593209325933093359340112233445
869345935093559360936593709375938093859390112233445
879395940094059410941594209425943094359440011223344
889445945094559460946594699474947994849489011223344
899494949995049509951395189523952895339538011223344
N0123456789123456789
909542954795529557956295669571957695819586011223344
919590959596009605960996149619962496289633011223344
929638964396479652965796619666967196759680011223344
939685968996949699970397089713971797229727011223344
949731973697419743975097549759976397689773011223344
959777978297869791979598009805980998149818011223344
969823982798329836984198459850985498599863011223344
979868987298779881988698909894989999039908011223344
989912991799219926993099349939994399489952011223344
999956996199659969997499789983998799919996011223334


Page compiled: Wed Sep 05 18:37:57 GMT+01:00 2001