Logarithms
by David M. Lane
Prerequisites
• Chapter 1: Distributions
Learning Objectives
- Compute logs using different bases
- Convert between bases
- State the relationship between logs and proportional change
The log transformation reduces positive skew. This can be valuable both for making the data more interpretable and for helping to meet the assumptions of inferential statistics.
Basics of Logarithms (Logs)
Logs are, in a sense, the opposite of exponents. Consider the following simple expression:
102 = 100
Here we can say the base of 10 is raised to the second power. Here is an example of a log:
Log10(100) = 2
This can be read as: The log base ten of 100 equals 2. The result is the power that the base of 10 has to be raised to in order to equal the value (100). Similarly,
Log10(1000) = 3
since 10 has to be raised to the third power in order to equal 1,000.
These examples all used base 10, but any base could have been used. There is a base which results in “natural logarithms” and that is called e and equals approximately 2.718. It is beyond the scope of this book to explain what is “natural” about it. Natural logarithms can be indicated either as: Ln(x) or loge(x)
Changing the base of the log changes the result by a multiplicative constant. To convert from Log10 to natural logs, you multiply by 2.303. Analogously, to convert in the other direction, you divide by 2.303.
