# Logarithms

## What is a Logarithm?

## Video

This video from *Khan Academy* gives a nice explanation of what a logarithm is by comparing expressions involving logarithms to those involving indices.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

## Notes

These notes from MathCentre define logarithms. They also have exercises with answers included for you to get practice working with logarithms.

A pdf of this document can be downloaded here.

## Interactive Exercises

This NUMBAS exercise lets you test your understanding of the definition of a logarithm.

Please click here to view this NUMBAS question in another window.

## The Laws of Logarithms

## Video

This video from *Khan Academy* shows how to simplify the logarithm of a product of terms.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

This video from *Khan Academy* shows how to simplify a term involving the logarithm of a power.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

## Notes

These notes from MathCentre list the various properties of logarithms and show how they can be used to simplify expressions. There are also exercises included with answers for you to use for practice.

A pdf of this document can be downloaded here.

## Changing the Base of a Logarithm

## Videos

This video from *patrickJMT* shows how to use the change of base formula to compute the value of a logarithm.

Note: All *patrickJMT* content is available for free at www.youtube.com/user/patrickJMT.

Patrick JMT’s Website: www.patrickjmt.com.

## Notes

These notes from MathCentre gives the change of base law for logarithms, which allows you to write a logarithm in one base in terms of a logarithm of another base. There are also exercises with answers included for you to practise with.

A pdf of this document can be downloaded here.

## Interactive Exercises

Use this NUMBAS exercise to practise rewriting logarithms in terms of another base.

Please click here to view this NUMBAS question in another window.