Step by step
The question
Question: solve 5 times 2 to the power x = 40.
x is up in the power.
Careful!
The power is only on the 2.
Powers come before times.
So we can't join 5 and 2 first.
1 Get the power alone
First the power must be alone: nothing added to it, nothing times it.
The power is times 5.
To remove times 5, we divide by 5.
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.
5 divided by 5 is 1.
So just the power is left.
40 divided by 5 is 8.
Now we have 2ˣ = 8.
2 Write 8 as a power of 2
8 is 2 times itself, 3 times.
So 8 is 2³.
Now both sides are 2 to a power.
3 The powers are equal
Both sides are 2 to a power.
Same base, and they are equal.
So the powers must be equal too.
So x = 3!
4 Check
Let's check in the question: put 3 in place of x.
We get 40, the same as the right side.
So x = 3 is right!
Let's look back.
First: get the power alone.
Then: write 8 as a power of 2.
Then: the powers are equal.
Last: check.