Step by step
The question
Question: solve ln(x) = 2.
ln(x) = 2
e is a special number, like π.
It is about 2.718.
A log with base e is written ln.
We say "natural log".
e ≈ 2.718
ln = loge
1 Write it as a power
A log is a power.
ln(x) = 2 means: e to the power 2 is x.
ln c = k means ek = c
So x is e².
x = e2
Careful!
ln is log base e, not base 10.
So it is e to the power 2, not 10 to the power 2.
Careful: not x = 102 ✗
2 Use a calculator
With a calculator, e to the power 2 is about 7.3891.
e2 ≈ 7.3891
So x is about 7.389.
x ≈ 7.389
So x = e², about 7.389 to three decimal places.
3 Check
Let's check with a calculator.
ln 7.389 is about 2.00.
That is 2.
It works!
Check: ln(7.389) ≈ 2.00
Let's look back.
First: write it as a power.
Then: use a calculator.
Last: check.
Answer
x ≈ 7.389