Solve 2^(x+1) = 32

Step by step

The question

Question: solve 2 to the power (x + 1) = 32.

x is up in the power.

1 Write 32 as a power of 2

32 is 2 times itself, 5 times.

So 32 is 2⁵.

Now both sides are 2 to a power.

2 The powers are equal

Both sides are 2 to a power.

Same base, and they are equal.

So the powers must be equal too.

Now we have x + 1 = 5.

3 Remove the + 1

We want x by itself.

The + 1 is in the way.

To remove + 1, we take away 1.

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.

+ 1 and − 1 make zero.

Cross them out.

5 − 1 = 4.

So x = 4!

4 Check

Let's check: put 4 in place of x.

We get 32, the same as the right side.

So x = 4 is right!

Let's look back.

First: write 32 as a power of 2.

Then: the powers are equal.

Then: remove the + 1.

Last: check.