Logarithm
The
logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 10 to the power 3 is 1000: 1000 = 10 × 10 × 10 = 103. More generally, for any two real numbers
b and
x where
b is positive and
b ≠ 1, The logarithm to base 10 is called the common logarithm and has many applications in science and engineering. The natural logarithm has the irrational number
e as its base; its use is widespread in pure mathematics, especially calculus. The binary logarithm uses base 2 and is prominent in computer science. Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations. They were rapidly adopted by navigators, scientists, engineers, and others to perform computations more easily, using slide rules and logarithm tables.