Step by step
The question
Question: solve ln(x) = 1.
ln(x) = 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".
e ≈ 2.718
ln = loge
1 Write it as a power
A log is a power.
ln(x) = 1 means: e to the power 1 is x.
ln c = k means ek = c
So x is e¹.
x = e1
Careful!
ln is log base e, not base 10.
So it is e to the power 1, not 10 to the power 1.
Careful: not x = 101 ✗
2 Use a calculator
With a calculator, e to the power 1 is about 2.7183.
e1 ≈ 2.7183
So x is about 2.718.
x ≈ 2.718
So x = e¹, about 2.718 to three decimal places.
3 Check
Let's check with a calculator.
ln 2.718 is about 1.00.
That is 1.
It works!
Check: ln(2.718) ≈ 1.00
Let's look back.
First: write it as a power.
Then: use a calculator.
Last: check.
Answer
x ≈ 2.718