Step by step
The question
Question: solve 2 times 3 to the power x, − 4 = 50.
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.
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.
50 + 4 is 54.
Now we have 2 × 3ˣ = 54.
The power is times 2.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just the power is left.
54 divided by 2 is 27.
Now we have 3ˣ = 27.
2 Write 27 as a power of 3
27 is 3 times itself, 3 times.
So 27 is 3³.
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.
So x = 3!
4 Check
Let's check in the question: put 3 in place of x.
We get 50, the same as the right side.
So x = 3 is right!
Let's look back.
First: get the power alone.
Then: write 27 as a power of 3.
Then: the powers are equal.
Last: check.