*54*

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 R according to their base:

Base | Number | Log | Antilog |
---|---|---|---|

n | x | log(x, n) | x^n |

e | x | log(x) | exp(x) |

10 | x | log10(x) | 10^x |

The following examples show how to calculate the antilog of values in R 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:

#define original value original = 7 #take log (base 10) of original value log_original = log10(original) #display log (base 10) of original value log_original [1] 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 [1] 7

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 = 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 exp(log_original) [1] 7

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

**Example 3: Calculating the Antilog of Base x**

Suppose we take the log (base 5) of the value 7:

#define original value original = 7 #take log (base 5) of original value log_original = log(original, 5) #display log (base 10) of original value log_original [1] 1.209062

In order to get back the original value of 7, we can take the antilog by raising 5 to the power of 1.209062:

#take the antilog 5^log_original [1] 7

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

**Additional Resources**

How to Transform Data in R (Log, Square Root, Cube Root)

How to Perform a Box-Cox Transformation in R

How to Create a Log-Log Plot in R