Step by step
The question
Question: work out log₂ 32.
log2 32
There are four choices.
First we solve it, the normal way.
Then we pick.
1 What the log asks
log₂ 32 asks: 2 to what power is 32?
2 is the base: the number we raise to a power.
So a log is a power.
a log is a power
2 to the power what is 32?
2? = 32
2 Find the power
2 times 2 times 2 times 2 times 2 is 32.
That is 5 2's.
2 × 2 × 2 × 2 × 2 = 32
So the power is 5.
25 = 32
So log₂ 32 = 5.
log2 32 = 5
3 Pick the choice
Our answer is log₂ 32 = 5.
That is choice A.
A) 5
4 Why not the others
B is 16.
Wrong: 32 ÷ 2: a log asks for the power, 2 to what = 32.
B) 16 ✗ 32 ÷ 2: a log asks for the power, 2 to what = 32
C is 30.
Wrong: 32 − 2.
C) 30 ✗ 32 − 2
D is 64.
Wrong: 32 × 2.
D) 64 ✗ 32 × 2
Let's look back.
First: what the log asks.
Then: find the power.
Then: pick the choice.
Last: why not the others.
Answer
log2 32 = 5