How to Find the Antilog of Values in R


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

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