*53*

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:

log_{10}(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