What are Logarithms?

• Answers the question:
  • How many of one number do we multiply to get another number?

Example 1

How many 2s do we multiply to get 8?

2 × 2 × 2 = 8

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

log₂(8) = 3

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

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

Example 2

log₅(625) = ?

5 × 5 × 5 × 5 = 625

log₅(625) = 4

Example 3

log₂(64) = ?

2 × 2 × 2 × 2 × 2 × 2 = 64

log₂(64) = 6