Talk:Common logarithm

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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. CyborgTosser 09:55, 17 May 2004 (UTC)

Contents

[edit] More on Mantissas?

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 with 99 going by 1s. The top has numbers from 0 through 9 going by 1s also. As such, it looks like this:

N    0    1    2    3   ... 9
10 0000 0043 0086 0128  ...
11 0414 0453 0492 0531  ...
12 0792 0828 0864 0899  ...
13 1139 1173 1206 1239  ...
14 1461 1492 1523 1553  ...
15 1761 1790 1818 1847  ...
16 2041 2068 2095 2122  ...
17 2304 2330 2355 2380  ...
18 2553 2577 2601 2625  ...
19 2788 2810 2833 2856  ...
.    .    .    .    .
.    .    .    .    .
.    .    .    .    .
99

Anyway, I was just kind of hoping someone could explain it to me...

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 log10 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 log10 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 characteristic and 1818 is the mantissa. Michael Hardy 01:15, 11 July 2005 (UTC)




Thank you.

[edit] explanation

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.

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 to calculators. i'd love to see this issue fleshed out a bit.

s (unsigned by User:24.89.202.141)

Does the explanation at logarithm#Easier computations help? Maybe there should be a mention here to look at the explanation there. Gene Nygaard 19:11, 10 October 2005 (UTC)


[edit] Originator

Should this article discuss who invented Common logarithms? I think it was Henry Briggs. --maru (talk) contribs 16:35, 26 January 2006 (UTC)

[edit] Algorithm for log10(x)

Not that anyone gives a damn but here is an algorithm for calculating log10(x)

#!/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 >= 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 > epsilon:
    while X >= 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)

[edit] Further notation

My old mathematics teacher at school also led me to believe that while ln is a standard abbreviation of loge, lg was an accepted abbreviation of log10. Has anyone else seen lg used?

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. Michael Hardy 21:52, 24 May 2006 (UTC)
Yes, in computer science lg generally denotes log base 2. —Steven G. Johnson 04:03, 25 May 2006 (UTC)

[edit] Hilarious

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 on Wikipedia.

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