Use the definition of a logarithm to establish and apply the laws of logarithms (ACMNA265)

LO: To know and use the definition of logarithms and apply the laws of logarithms.


  • What is a log number
  • What are the laws of logarithm


  • that the laws of logarithms helps us to simplify scenarios


  • I know and can apply the law of logarithms to solve related problems.

Examples (Visual Representations)


What are logarithms?

Logarithms are essentially the opposite to exponents or indices. It answers the question of how much of a certain number do we need to multiply in order to get another number?

When working with numbers, we have a base (original number), we have an exponent or indices (little number) and then we have an answer.

In this example, we have a base of 5 and exponent of 3 and an answer of 125. Which mean it takes three – 5s multiplied by each other in order to get to 125.

When working with Logs you are essentially rearranging the order where the numbers are located.

Logarithm Laws

We have some established logarithm laws. They are very similar to the index laws that we’ve learnt previously.

When we add logarithms with the same base we can simplify it into m x n.

When we subtract logarithms with the same base we can simplify it into m / n.

Logarithm Videos

Logarithm Resources

BBC Bitesize Logarithms
Purple Maths – Logarithms
Maths is Fun – Logarithms

Practice Questions

My Maths 10/10A

pg. 141 Exercise 3G Q. 1-7

pg. 147 Exercise 3H Q. 7-13, 16-18*