Step by step
The question
Question: solve 5 to the power x, − 4 = 21.
x is up in the power.
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 − 4 is in the way.
To remove − 4, we add 4.
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.
− 4 and + 4 make zero.
Cross them out.
21 + 4 is 25.
Now we have 5ˣ = 25.
2 Write 25 as a power of 5
25 is 5 times itself, 2 times.
So 25 is 5².
Now both sides are 5 to a power.
3 The powers are equal
Both sides are 5 to a power.
Same base, and they are equal.
So the powers must be equal too.
So x = 2!
4 Check
Let's check in the question: put 2 in place of x.
We get 21, the same as the right side.
So x = 2 is right!
Let's look back.
First: get the power alone.
Then: write 25 as a power of 5.
Then: the powers are equal.
Last: check.