Solve 2^x + 5 = 37 Step by Step | Exponential equations

Step by step

The question

Question: solve 2 to the power x, + 5 = 37.

x is up in the power.

2^x + 5 = 37

1 Get the power alone

First the power must be alone: nothing added to it, nothing times it.

first: the power alone

We want the power by itself.

The + 5 is in the way.

To remove + 5, we take away 5.

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^x ~~+ 5 − 5~~ = 37 − 5

+ 5 and − 5 make zero.

Cross them out.

37 − 5 is 32.

Now we have 2ˣ = 32.

2^x = 32

2 Write 32 as a power of 2

32 is 2 times itself, 5 times.

2 × 2 × 2 × 2 × 2 = 32

So 32 is 2⁵.

Now both sides are 2 to a power.

2^x = 2⁵

3 The powers are equal

Both sides are 2 to a power.

Same base, and they are equal.

So the powers must be equal too.

same base → same power

So x = 5!

x = 5

4 Check

Let's check in the question: put 5 in place of x.

Check: 2⁵ + 5 = 32 + 5 = 37

We get 37, the same as the right side.

So x = 5 is right!

Let's look back.

First: get the power alone.

Then: write 32 as a power of 2.

Then: the powers are equal.

Last: check.

Answer