Calculate log_2(4 × 8)

Step by step

The question

Question: work out log₂(4 × 8).

We use a log rule.

1 Use the product rule

The product rule: times inside the log becomes plus outside.

Why?

A log is a power.

4 is 2², and 8 is 2³.

Multiplying adds the powers.

So log₂(4 × 8) is log₂ 4 plus log₂ 8.

2 Work out each log

log₂ 4 is 2, because 2² is 4.

log₂ 8 is 3, because 2³ is 8.

So we get 2 plus 3.

2 plus 3 is 5.

So log₂(4 × 8) = 5.

3 Check

Let's check: work out the inside first.

4 times 8 is 32.

log₂ 32 is 5, because 2⁵ is 32.

Same answer!

Let's look back.

First: use the product rule.

Then: work out each log.

Last: check.