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# Logarithms

Logarithms (Greek, â€˜number-reckoningâ€™) were first used in the 18th century; invented by John Napier (1550 - 1617), they were the first major advance in methods of carrying out complicated arithmetical calculations in a long line leading to modern computational techniques.

In the equation y = xm, the number m is known as the logarithm of y in the base x. The reason that logarithms aid calculations is that if y = xm, z = xn then y Ã— z = xm Ã— xn = xm + n, so that the logarithm of the product is the sum of the logarithms. Division can also be performed in the same way by subtraction. It is far simpler to work out the sum or difference of two numbers than to do a complicated long division or long multiplication.

Logarithms are published in books. To multiply a by b, you look up the logs of a and b (to give log (a + b)), then look up the antologarithm, which gives you the answer. Slide rules even do the addition for you or, in the case of division, the subtraction of log b from log a. Before electronic calculators, these were indispensable tools of mathematicians, scientists and technologists. SMcL

##### Logic

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