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In its simplest form, a logarithm answers the question: How many of one number multiply together to make another number?

For example:

How many 2s multiply together to make 8?

Answer: 2 × 2 × 2 = 8, so we had to multiply 3 of the 2s to get 8

So the logarithm is 3

We write it like this:

log₂(8) = 3

Notice we are dealing with three numbers:

the base: the number we are multiplying (a "2" in the example above)

how often to use it in a multiplication (3 times, which is the logarithm)

The number we want to get (an "8")

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Before you start this part, I hope you have completed all the work associated with Indices, as this section might be a bit tricky without it!

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Logarithms - Laws of Logarithms (Live Lecture)

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Transpose to the letter indicated on the RHS