**Logarithm**

**LOG'ARITHM**, *noun* [Gr. ratio, and number.]

Logarithms are the exponents of a series of powers and roots.

The *logarithm* of a number is that exponent of some other number, which renders the power of the latter, denoted by the exponent, equal to the former.

When the logarithms form a series in arithmetical progression, the corresponding natural numbers form a series in geometrical progression. Thus,

Logarithms

0 1 2 3 4 5

Natural numbers, 1 10 100 1000 10000 100000

The addition and subtraction of logarithms answer to the multiplication and division of their natural numbers. In like manner, involution is performed by multiplying the *logarithm* of any number by the number denoting the required power; and evolution, by dividing the *logarithm* by the number denoting the required root.

Logarithms are the invention of Baron Napier, lord of Marchiston in Scotland; but the kind now in use, were invented by Henry Briggs, professor of geometry in Gresham college at Oxford. They are extremely useful in abridging the labor of trigonometrical calculations.