Logarithms Logarithms were discovered by the Scottish mathematician John Napier in 1614. The theory of logarithms is one of the most important theories in the whole of maths because it makes multiplication and division of large numbers a lot easier (especially when done with a slide rule). Before the invention of electronic calculators logarithms were used to do all multiplication and division of large numbers. All school children were taught about logarithms and how to use a slide rule until about 25 years ago. The theory of logarithms states that one number multiplied by another number is equal to the log of the first number added to the log of the second number. If you know the logs of two numbers, by looking them up in a table, it is simple to multiply them. For example, if you want to multiply 386,927,560 by 592,674,820 all you have to do is look up the log of 386,927,56 in a table of logarithms, which gives 8.59, and the log of 592,674,820, which is 8.77. Add them together, which makes 17.36, and then look up the number that the combined logs correspond to in the same table: 17.36 corresponds to 229,322,221,976,039,200. The same thing works for division, only instead of adding the logs of the two number you subtract them.