Step by step
The question
Question: solve 5 to the power (2x) = 125.
x is up in the power.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Write 125 as a power of 5
We want both sides to be 5 to a power.
Is 125 made of 5's?
125 is 5 times 5 times 5: 3 5's multiplied.
So 125 is 5³.
Now both sides are 5 to a power.
2 The powers are equal
Both sides are 5 to a power.
5 is the base: the number under the power.
Same base, and the two sides are equal.
So the powers must be equal too.
Each power gives a different number: 25, 125, 625.
So a different power would give a different number.
Now we have 2x = 3.
Is x alone now?
Not yet: 2x means 2 times x.
How do we remove it?
3 Remove the 2
To remove times 2, we divide by 2.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
2 divided by 2 is 1.
They cancel each other.
So just x is left.
So x = 3/2!
4 Check
Let's check: put 3/2 in place of x.
We get 125, the same as the right side.
So x = 3/2 is right!
5 Pick the choice
Our answer is x = 3/2.
That is choice A.
6 Why not the others
B is 3.
Wrong: that is 2x, not x.
C is 12.5.
Wrong: 125 ÷ 10: 5²ˣ is not 10x.
D is 25.
Wrong: 125 ÷ 5: 125 is 5³.
Let's look back.
First: write 125 as a power of 5.
Then: the powers are equal.
Then: remove the 2.
Then: check.
Then: pick the choice.
Last: why not the others.