Logarithms were invented independently by John Napier, a Scotsman, and by Joost Burgi, a Swiss. The logarithms which they invented differed from each other and from the common and natural logarithms now in use. Napier's logarithms were published in 1614; Burgi's logarithms were published in 1620. The objective of both men was to simplify mathematical calculations. Napier's approach was algebraic and Burgi's approach was geometric. Neither men had a concept of a logarithmic base. Napier defined logarithms as a ratio of two distances in a geometric form, as opposed to the current definition of logarithms as exponents. The possibility of defining logarithms as exponents was recognized by John Wallis in 1685 and by Johann Bernoulli in 1694.

The invention of the common system of logarithms is due to the combined effort of Napier and Henry Briggs in 1624. Natural logarithms first arose as more or less accidental variations of Napier's original logarithms. Their real significance was not recognized until later. The earliest natural logarithms occur in 1618.

EVERYDAY USE OF LOGARITHMS

USED IN PHASE SUCH AS : 6 FIGURE SALARY, DOUDLE-DIGIT EXPENSE, INTEREST RATE

Now that calculators and computers are common, logarithms are still very, very useful, but in a totally different way. They are very closely related to exponential functions. For example, you probably know by now that y = a^x is equivalent to log_a(y) = x, where log_a(y) is the base a logarithm of y. The