Calculate log_2(8^2)

Step by step

The question

Question: work out log₂(8²).

We use a log rule.

1 Use the power rule

The power rule: a power inside the log comes down in front, as times.

Why?

A log is a power.

8 is 2³.

A power of a power multiplies the powers.

So the 2 comes out as times.

So log₂(8²) is 2 times log₂ 8.

2 Work out the log

log₂ 8 is 3, because 2³ is 8.

So it is 2 times 3.

2 times 3 is 6.

So log₂(8²) = 6.

3 Check

Let's check: work out the inside first.

8² is 64.

log₂ 64 is 6, because 2⁶ is 64.

Same answer!

Let's look back.

First: use the power rule.

Then: work out the log.

Last: check.