Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum » !Ignotum/Formulae/Loga
!Ignotum/Formulae/Loga
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum |
| Filename: | !Ignotum/Formulae/Loga |
| Read OK: | ✔ |
| File size: | 0214 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
# Maths > Logarithms If log<a>b=c then b=a^c The most basic rule of logarithms, where b & c are numbers and <a> is the base. The base is usually 10 or the constant e (2.718). Log<e>x is written as lnx. Log<10>x is usually just written as logx. log(a^b)=bloga log(ab)=loga+logb log(a/b)=loga-logb log<b>a=log<c>a/log<c>b This is the easiest way to change the logarithm base. log<a>b=1/log<b>a
00000000 23 20 4d 61 74 68 73 20 3e 20 4c 6f 67 61 72 69 |# Maths > Logari| 00000010 74 68 6d 73 0a 49 66 20 6c 6f 67 3c 61 3e 62 3d |thms.If log<a>b=| 00000020 63 20 74 68 65 6e 20 62 3d 61 5e 63 0a 54 68 65 |c then b=a^c.The| 00000030 20 6d 6f 73 74 20 62 61 73 69 63 20 72 75 6c 65 | most basic rule| 00000040 20 6f 66 20 6c 6f 67 61 72 69 74 68 6d 73 2c 20 | of logarithms, | 00000050 77 68 65 72 65 0a 62 20 26 20 63 20 61 72 65 20 |where.b & c are | 00000060 6e 75 6d 62 65 72 73 20 61 6e 64 20 3c 61 3e 20 |numbers and <a> | 00000070 69 73 20 74 68 65 20 62 61 73 65 2e 20 54 68 65 |is the base. The| 00000080 0a 62 61 73 65 20 69 73 20 75 73 75 61 6c 6c 79 |.base is usually| 00000090 20 31 30 20 6f 72 20 74 68 65 20 63 6f 6e 73 74 | 10 or the const| 000000a0 61 6e 74 20 65 20 0a 28 32 2e 37 31 38 29 2e 20 |ant e .(2.718). | 000000b0 4c 6f 67 3c 65 3e 78 20 69 73 20 77 72 69 74 74 |Log<e>x is writt| 000000c0 65 6e 20 61 73 20 6c 6e 78 2e 0a 4c 6f 67 3c 31 |en as lnx..Log<1| 000000d0 30 3e 78 20 69 73 20 75 73 75 61 6c 6c 79 20 6a |0>x is usually j| 000000e0 75 73 74 20 77 72 69 74 74 65 6e 20 61 73 20 6c |ust written as l| 000000f0 6f 67 78 2e 0a 6c 6f 67 28 61 5e 62 29 3d 62 6c |ogx..log(a^b)=bl| 00000100 6f 67 61 0a 0a 0a 0a 0a 0a 6c 6f 67 28 61 62 29 |oga......log(ab)| 00000110 3d 6c 6f 67 61 2b 6c 6f 67 62 0a 20 0a 0a 0a 0a |=loga+logb. ....| 00000120 0a 6c 6f 67 28 61 2f 62 29 3d 6c 6f 67 61 2d 6c |.log(a/b)=loga-l| 00000130 6f 67 62 0a 0a 0a 0a 0a 0a 6c 6f 67 3c 62 3e 61 |ogb......log<b>a| 00000140 3d 6c 6f 67 3c 63 3e 61 2f 6c 6f 67 3c 63 3e 62 |=log<c>a/log<c>b| 00000150 0a 54 68 69 73 20 69 73 20 74 68 65 20 65 61 73 |.This is the eas| 00000160 69 65 73 74 20 77 61 79 20 74 6f 20 63 68 61 6e |iest way to chan| 00000170 67 65 20 74 68 65 0a 6c 6f 67 61 72 69 74 68 6d |ge the.logarithm| 00000180 20 62 61 73 65 2e 0a 0a 0a 0a 6c 6f 67 3c 61 3e | base.....log<a>| 00000190 62 3d 31 2f 6c 6f 67 3c 62 3e 61 0a 0a 0a 0a 0a |b=1/log<b>a.....| 000001a0 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |................| * 00000210 0a 0a 0a 0a |....| 00000214
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