Intro to Logarithms            Page 3 of 3

​Common Logarithms - Base 10

A logarithm can have any positive number as the base. One of the most common bases for a logarithm is base 10.  When a logarithm has a 10 as the base, it's called a common logarithm.  If a logarithm is written without a base - without a little subscript number written - you can assume that the base is 10.

Most calculators have a button for a common logarithm.  Look for the "log" button on your calculator.  If you type in log(100), it should say the answer is 2 because 10 to the second power equals 100.​ 

​Natural Logarithms - Base e

​Another number that's commonly used as the base of a logarithm is the number e.  e is an irrational number that comes up so often that it gets it's own symbol (similar to how the number 3.14159. .  is called pi).  The constant e is named after the mathematician Leonhard Euler. It is approximately equal to 2.718.  When a logarithm has a base of e, it's called a natural logarithm.  This is abbreviated as ln  (that's a lowercase L. l for log, n for natural).

Most calculators also have a button to calculate a natural logarithm.  Look for the "ln" button on your calculator.  Remember, it's a lowercase L for log and the letter n to indicate a natural log.

Practice

Ready to try answering some questions about logarithms on your own? Click the START button below to try some on your own!

Powered by Interact

Interested in learning more about logarithms? Check out the lessons on solving equations with logarithms, logarithm rules, or the change of base formula.

 1      2      3