antilogarithm

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 mathematically as if log_b(y) = x, then antilog_b(x) = y. This is equivalent to y = b^x. Essentially, finding the antilogarithm means raising the base of the logarithm to the power of the given number.

For example, if we consider the common logarithm (base 10), the logarithm of 100 is 2, because 10^2 = 100. Therefore, the antilogarithm of 2 to the base 10 is 100. Similarly, the natural logarithm (base e, where e is approximately 2.71828) of e^3 is 3. The antilogarithm of 3 to the base e is e^3, which is approximately 20.0855.

The term antilogarithm is less commonly used today, as the concept is directly understood as exponentiation. However, it was historically significant, particularly before the widespread availability of calculators and computers, as it was used in conjunction with logarithm tables to simplify complex multiplication and division problems. By converting numbers into their logarithms, one could perform multiplication through addition and division through subtraction, then use antilogarithms to convert the result back to the original scale.