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 e⁻¹.
x = e−1
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 = 10−1 ✗
2 Use a calculator
With a calculator, e to the power −1 is about 0.3679.
e−1 ≈ 0.3679
So x is about 0.368.
x ≈ 0.368
So x = e⁻¹, about 0.368 to three decimal places.
3 Check
Let's check with a calculator.
ln 0.368 is about −1.00.
That is −1.
It works!
Check: ln(0.368) ≈ −1.00
Let's look back.
First: write it as a power.
Then: use a calculator.
Last: check.
Answer
x ≈ 0.368