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 3

^{4}= 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 10^{x} = 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 = 10
^{5}= 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 10^{x} key (for base 10) and e^{x} (for base e).

It’s good practice to keep the same number of significant figures when finding antilogarithms [3]. For example,

log(3 x 10^{4}) = 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