How to Find the Antilog of Values in Python


The antilog of a number is the inverse of the log of a number.

So, if you calculate the log of a number you can then use the antilog to get back the original number.

For example, suppose we start with the number 7. If we take the log (base 10) of 7 then we would get .845:

log10(7) = .845

The antilog (base 10) of the value 0.845 can be found by taking 10 raised to the power of 0.845:

10.845 = 7

The antilog allowed us to get back the original number.

The following table shows how to calculate the antilog of values in Python according to their base:

Base Number Log Antilog
e x np.log(x) np.exp(x)
10 x np.log10(x) 10 ** x

The following examples show how to calculate the antilog of values in Python using different values for the base.

Example 1: Calculating the Antilog of Base 10

Suppose we take the log (base 10) of the value 7:

import numpy as np

#define original value
original = 7

#take log (base 10) of original value
log_original = np.log10(original)

#display log (base 10) of original value
log_original

0.845098

In order to get back the original value of 7, we can take the antilog by raising 10 to the power of 0.845098:

#take the antilog
10 ** log_original

7.0

By taking the antilog, we were able to obtain the original value of 7.

Example 2: Calculating the Antilog of a Natural Log

Suppose we take the natural log of the value 7:

#define original value
original = 7

#take natural log of original value
log_original = np.log(original)

#display natural log of original value
log_original

[1] 1.94591

In order to get back the original value of 7, we can take the antilog by raising e to the power of 1.94591:

#take the antilog
np.exp(log_original)

7.0

By taking the antilog, we were able to obtain the original value of 7.

Additional Resources

How to Create a Log-Log Plot in Python
How to Perform a Box-Cox Transformation in Python

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