Step by step
The question
Question: solve 4 times 2 to the power x, − 8 = 24.
x is up in the power.
Careful!
The power is only on the 2.
Powers come before times.
So we can't join 4 and 2 first.
1 Get the power alone
First the power must be alone: nothing added to it, nothing times it.
We want the power by itself.
The − 8 is in the way.
To remove − 8, we add 8.
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.
− 8 and + 8 make zero.
Cross them out.
24 + 8 is 32.
Now we have 4 × 2ˣ = 32.
The power is times 4.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just the power is left.
32 divided by 4 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 24, 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.