Solve 2^x - 3 = 13 Step by Step | Exponential equations

Step by step

The question

Question: solve 2 to the power x, − 3 = 13.

x is up in the power.

2^x − 3 = 13

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 − 3 is in the way.

To remove − 3, we add 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.

2^x ~~− 3 + 3~~ = 13 + 3

− 3 and + 3 make zero.

Cross them out.

13 + 3 is 16.

Now we have 2ˣ = 16.

2^x = 16

2 Write 16 as a power of 2

16 is 2 times itself, 4 times.

2 × 2 × 2 × 2 = 16

So 16 is 2⁴.

Now both sides are 2 to a power.

2^x = 2⁴

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 = 4!

x = 4

4 Check

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

Check: 2⁴ − 3 = 16 − 3 = 13

We get 13, the same as the right side.

So x = 4 is right!

Let's look back.

First: get the power alone.

Then: write 16 as a power of 2.

Then: the powers are equal.

Last: check.

Answer