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This is just another word for index or power. So 32 = 9 means the logarithm is 2, with base 3 gives 9.

This can also be written as 2 = log39

In general, remember that logab = c ⇔ b = ac

Logarithm Laws

You need to know that

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Here are some examples:


You may be asked to find the values of expressions without the use of tables. Here, you change the base to 10 as shown in this example:

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We've changed the base from 5 to 10 and now can use a calculator to find log53.

Remember: that we change from base a to base b by using this formula:

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These are equations where the variable is an index, an example is 3x= 6.

The steps to the solution are:

Step 1: Take logs of both sides:

So, using the law of logarithms:

log 3x = log 6
x log 3 = log 6

Step 2: Make x the subject:

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Step 3: Use a calculator to find x to 3 signifcant figures (sf).


Solve the equation 22x = 5.

Step 1: Take logs of both sides

2x log 2 = log 5

Step 2: Make x the subject

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Step 3: Use a calculator to find the value of x

x = 1.16 (3sf)

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