What is the value of log_5(125)?

Step by step

The question

Question: work out log₅ 125.

There are four choices.

First we solve it, the normal way.

Then we pick.

1 What the log asks

log₅ 125 asks: 5 to what power is 125?

5 is the base: the number we raise to a power.

So a log is a power.

5 to the power what is 125?

2 Find the power

We go up the powers of 5 until we reach 125: 5, 25, 125.

5³ is 125.

So the power is 3.

So log₅ 125 = 3.

3 Pick the choice

Our answer is log₅ 125 = 3.

That is choice A.

4 Why not the others

B is 25.

Wrong: 125 ÷ 5: a log asks for the power, 5 to what = 125.

C is 120.

Wrong: 125 − 5.

D is 625.

Wrong: 125 × 5.

Let's look back.

First: what the log asks.

Then: find the power.

Then: pick the choice.

Last: why not the others.