Solve ln(2x) = 1

Step by step

The question

Question: solve ln(2x) = 1.

e is a special number, like π.

It is about 2.718.

A log with base e is written ln.

We say "natural log".

1 Write it as a power

A log is a power.

ln(2x) = 1 means: e to the power 1 is 2x.

So 2x is e¹.

Careful!

ln is log base e, not base 10.

So it is e to the power 1, not 10 to the power 1.

2 Remove the 2

2x means 2 times x.

We want just x.

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 x is left.

So x = e¹ over 2.

This is the exact answer.

3 Use a calculator

With a calculator, e to the power 1 is about 2.7183.

Then 2.7183 ÷ 2 is about 1.359.

So x is about 1.359.

So x = e¹ over 2, about 1.359 to three decimal places.

4 Check

Let's check with a calculator.

The inside is about 2.718.

ln of it is about 1.00.

That is 1.

It works!

Let's look back.

First: write it as a power.

Then: remove the 2.

Then: use a calculator.

Last: check.