# Antilogarithm: Definition, Examples

An antilogarithm is another name for an exponential function. It reverses the procedure of taking a logarithm [1].

If x = log b, then antilog (x) = b.

The word “antilogarithm” is just another word for “number” or “result”. For example, in the expression 34 = 81, the result “81” is the antilogarithm [2]

For base 10 logarithms, the antilog is the result you get when you raise 10 to that number. For example, the antilogarithm of X is 10x = N.

## Antilogarithm Examples

Although you can’t take the logarithm of zero or negative numbers, you can take the antilog. The antilogarithm of integers are relatively easy to find by hand. Assuming base 10 logarithm, we have:

• antilog 5 = 105 = 100,000
• antilog -4 = 10-4 = 0.0001
• antilog 0 = 100 = 1

On many calculators (especially scientific and graphing calculators), the antilog button is the 10x key (for base 10) and ex (for base e).

It’s good practice to keep the same number of significant figures when finding antilogarithms [3]. For example,
log(3 x 104) = 4.477121, so round to 4.5

## References

[1] Introduction. Retrieved May 7, 2022 from: https://foothill.edu/psme/daley/tutorials_files/03.%20Logarithms.pdf
[2] PubHtlh 540 Introductory Biostatistics: Review of Logarithms and Exponents. Retrieved May 7, 2022 from: http://people.umass.edu/biep540w/pdf/logarithms%20and%20antilogaritms.pdf
[3] Logarithms and Antilogarithms. Retrieved May 7, 2021 from: http://alpha.chem.umb.edu/chemistry/ch115/Mridula/CHEM%20116/documents/LogarithmsandAntilogithms.pdf