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 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