An antilog is the inverse function of a logarithm. This notation was common when calculations were performed with slide rules or by referencing tables of numbers. Today, computers perform these calculations, and the use of the term "antilog" has been replaced in mathematics by the term "exponent." However, you still see the term "antilog" used in electronics for components such as antilog amplifiers.
TL;DR (Too Long; Didn't Read)
To calculate an antilogarithm of any number "x," you raise the logarithm base, "b," to the power of x, i.e. bx.
Define the Logarithm
Define a logarithm. The logarithm of a number is the power to which a given base must be raised to obtain that number. For example, you raise 10 to the power of 2 to obtain 100, so the base 10 logarithm of 100 is 2. You express this mathematically as log(10) 100 = 2.
Describe Inverse Function
Describe an inverse function. If a function f takes an input A and produces an output B and there is a function f-1 which takes an input B to produce A, we say that f-1 is the inverse function of f. It is important to note that when you see the notation f-1, interpret it as "f inverse;" don't treat it as an exponent.
Antilog = Inverse Log
Define an antilogarithm in terms of a logarithm. The antilogarithm is the inverse function of a logarithm, so log(b) x = y means that antilog (b) y = x. You write this with exponential notation such that antilog (b) y = x implies by = x.
Examine Antilog Notation
Examine a specific example of antilog notation. Because log(10) 100 = 2, antilog(10) 2 = 100 or 102 = 100.
Calculate an Antilog
Solve a specific antilog problem. Given log (2) 32 = 5, what is antilog (2) 5? 25 = 32, so antilog (2) 5 = 32.