Logarithm Laws and Properties | Maths Tutorials from an Oxford Graduate

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Learn how to use the laws of logarithms with an Oxford graduate. Logarithms can be very useful foir solving indicial equations or equations with unknown powers. To be able to do this, you need to know and be able to correctly apply the laws and properties of logarithms. This lesson explains where the rules come from and how and why they work, linking them to the laws of indices that you should already be familiar with. We will also look at some examples of how to use the laws and how to change the base of a logarithmic equation.

If you want to watch a specific part of the lesson, click on the following links to take you to the relevant part of the video:
A recap of what logarithms are: 0:21
Why logarithms and exponentials of the same base cancel each other out: 1:37
Why the logarithm of 1 to any base is 0: 4:03
Why the logarithm of b to base b is 1: 6:03
Test yourself on the basic properties of logarithms: 6:37
Why log(a) + log(b) = log(ab): 8:49
Why log(a) – log(b) = log(a/b): 13:07
Why log(a^x) = xlog(a): 15:39
How to use the laws of logarithms: 18:00
Test yourself on the laws of logarithms: 20:11
Why log(3x^2) does not equal 2log(3x) (a common mistake): 21:35
How to change the base: 23:48
How to use logs to solve an equation with an unknown power: 27:18
Test yourself on using the laws of logarithms in equations: 29:35

Previous knowledge required:

How to use the laws of indices: (coming soon)

Where to go next:

How to do logarithmic reduction: (coming soon)
How to solve problems involving unknown powers: (coming soon)

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OxMath provides easy to understand maths tutorials for learners, teachers and parents. The lessons are given by an Oxford Graduate with a First class Masters degree in Engineering, a PGCE in Maths and experience as a maths teacher at various schools and FE facilities.

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