Step by step
The question
Question: solve 2 times 5 to the power x, + 3 = 53.
x is up in the power.
Careful!
The power is only on the 5.
Powers come before times.
So we can't join 2 and 5 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 + 3 is in the way.
To remove + 3, we take away 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 and − 3 make zero.
Cross them out.
53 − 3 is 50.
Now we have 2 × 5ˣ = 50.
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.
50 divided by 2 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 53, 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.