Logarithm

Introduction to Logarithms

In its simplest form, a logarithm answers the question:

How many of one number do we multiply to get another number?

Example: How many 2s do we multiply to get 8?

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

So the logarithm is 3

How to Write it

We write "the number of 2s we need to multiply to get 8 is 3" as:

log₂(8) = 3

So these two things are the same:

The number we are multiplying is called the "base", so we can say:

• "the logarithm of 8 with base 2 is 3"
• or "log base 2 of 8 is 3"
• or "the base-2 log of 8 is 3"

Notice we are dealing with three numbers:

• the base: the number we are multiplying (a "2" in the example above)
• how many times to use it in a multiplication (3 times, which is the logarithm)
• The number we want to get (an "8")