Step by step
The question
Question: solve 2 times 3 to the power (2x) = 162.
x is up in the power.
Careful!
The power is only on the 3.
Powers come before times.
So we can't join 2 and 3 first.
1 Get the power alone
First the power must be alone: nothing added to it, nothing times it.
The power is times 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.
So just the power is left.
162 divided by 2 is 81.
Now we have 3 to the power (2x) = 81.
2 Write 81 as a power of 3
81 is 3 times itself, 4 times.
So 81 is 3⁴.
Now both sides are 3 to a power.
3 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 2x = 4.
4 Remove the 2
2x means 2 times x.
We want just x.
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.
So just x is left.
4 divided by 2 is 2.
So x = 2!
5 Check
Let's check in the question: put 2 in place of x.
We get 162, the same as the right side.
So x = 2 is right!
Let's look back.
First: get the power alone.
Then: write 81 as a power of 3.
Then: the powers are equal.
Then: remove the 2.
Last: check.