antilogarithms

An antilogarithm is the inverse operation of a logarithm. If the logarithm of a number y to a base b is x, then the antilogarithm of x to the base b is y. This can be expressed as: if log_b(y) = x, then antilog_b(x) = y. This is equivalent to saying that y = b^x.

The term antilogarithm is not frequently used in modern mathematics, as it is generally considered redundant. The operation of finding the antilogarithm is simply exponentiation. For example, if we know that the base-10 logarithm of 100 is 2 (log_10(100) = 2), then the antilogarithm of 2 to the base 10 is 100 (antilog_10(2) = 100). This is calculated by raising the base (10) to the power of the logarithm (2), resulting in 10^2 = 100.

Historically, antilogarithm tables were used in conjunction with logarithm tables to perform multiplication and division. By converting numbers to their logarithms, multiplication could be performed by adding the logarithms, and division by subtracting them. The antilogarithm was then used to convert the resulting sum or difference back to the original number. With the advent of calculators and computers, the use of such tables has become obsolete. The concept remains fundamental, however, as it underpins the relationship between logarithms and exponentiation.