Step by step
The question
Question: solve 27 to the power x = 9.
x is up in the power.
1 Write both as powers of 3
27 is 3³, and 9 is 3².
We write both as powers of 3.
So 27 becomes 3³, and 9 becomes 3².
A power of a power: multiply the powers.
The powers multiply: 3 times x is 3x.
2 The powers are equal
Both sides are 3 to a power.
Same base, and they are equal.
So the powers must be equal too.
Now we have 3x = 2.
3 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
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.
3 divided by 3 is 1.
So just x is left.
So x = 2/3!
4 Check
Let's check: put 2/3 in place of x.
We get 9, the same as the right side.
So x = 2/3 is right!
Let's look back.
First: write both as powers of 3.
Then: the powers are equal.
Then: remove the 3.
Last: check.