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 log_ab = c ⇔ b = a^c

Logarithm Laws

You need to know that

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:

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:

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

The steps to the solution are:

Step 1: Take logs of both sides:

So, using the law of logarithms:

Step 2: Make x the subject:

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

Example:

Solve the equation 2^2x = 5.

Step 1: Take logs of both sides

2x log 2 = log 5

Step 2: Make x the subject

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

x = 1.16 (3sf)