User:Milton Beychok/Sandbox
Before the advent of calculators and computers
The operations of addition and subtraction are much easier to perform than are the operations of multiplication and division. Logarithms were characterized by Pierre-Simon Laplace, the French mathematician and astronomer, as "doubling the life of an astronomer". The German mathematician, Karl Friedrich Gauss, who also did work in physics and astronomy, is said to have memorized a table of logarithms to save the time required to look up a logarithm each time he needed one.[1]
The use of logarithms was widespread because of their relative simplicity compared to multiplication, division, or raising numbers numbers to an exponential power. A few numerical examples, using base-10 logarithms (to eight decimal places) will illustrate that simplicity.
Example 1: Calculate 112.76 × 3,085.31 by using
- log10(112.76) + log10(3085.31 = 2.05215507 + 3.48929881 = 5.54145387
- antilog10(5.54145387) = 347,899.55
The answer would be 347,899.56 by using an electronic calculator.
Example 2: Calculate 47.53 ÷ 860.22 by using
- log10(47.53) − log10(860.22) = 1.67696781 − 2.93460954 = −1.25764172
- antilog10(−1.25764172) = 0.05525233
The answer would be 0.05525233 by using an electronic calculator.
Example 3: Calculate 963.641/3 using
- (1/3) × log10(963.64) = (1/3) × 2.98391482 = 0.99463827
- antilog10 (0.99463827) = 9.87730064
The answer would be 9.87730064 by using an electronic calculator.
Note: The antilog10 of x is simply 10x
- ↑ R.A. Rosenbaun and G.P. Johnson (1984). Calculus: Basic Concepts and Applications. Cambridge University Press. ISBN 0-521-25012-9.