Solve 3 × 2^(x + 1) = 48 Step by Step

Step by step

The question

Question: solve 3 times 2 to the power (x + 1) = 48.

x is up in the power.

3 × 2^{x + 1} = 48

Careful!

The power is only on the 2.

Powers come before times.

So we can't join 3 and 2 first.

Careful: not 3 × 2^{(x + 1)} = 6^{(x + 1)} ✗

1 Get the power alone

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

first: the power alone

The power is times 3.

To remove times 3, we divide by 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 × 2^{x + 1}3 = 483

3 divided by 3 is 1.

So just the power is left.

48 divided by 3 is 16.

Now we have 2 to the power (x + 1) = 16.

2^{x + 1} = 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 + 1} = 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

Now we have x + 1 = 4.

x + 1 = 4

4 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.

x ~~+ 1 − 1~~ = 4 − 1

+ 1 and − 1 make zero.

Cross them out.

4 − 1 = 3.

4 − 1 = 3

So x = 3!

x = 3

5 Check

Let's check in the question: put 3 in place of x.

Check: 3 × 2^{3 + 1} = 3 × 16 = 48

We get 48, the same as the right side.

So x = 3 is right!

Let's look back.

First: get the power alone.

Then: write 16 as a power of 2.

Then: the powers are equal.

Then: remove the + 1.

Last: check.

Answer