How to Calculate Antilog

The term "antilog" has been replaced in mathematics by the term "exponent."

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, the term "antilog" is still commonly used in electronics for certain components known as antilog amplifiers.

Difficulty:

Moderate

Instructions

Things You'll Need

• Calculator with exponent functions

1. 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, 10 must be raised to the power of 2 to obtain 100, so the base 10 logarithm of 100 is 2. This is expressed mathematically as log(10) 100 = 2.

2. 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 the notation f^-1 should be read as "f inverse" and should not be confused with an exponent.

3. 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. This is commonly expressed with exponential notation such that antilog (b) y = x implies b^y = x.

4. Examine a specific example of antilog notation. Because log(10) 100 = 2, antilog(10) 2 = 100 or 10^2 = 100.

5. Solve a specific antilog problem. Given log (2) 32 = 5, what is antilog (2) 5?

   2^5 = 32, so antilog (2) 5 = 32.

References

• Math Logarithms: Explaining Logarithms

Resources

• Read this Article in Spanish
• Mental Math