Step by step
The question
Question: work out ln(e²).
ln(e2)
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 What the log asks
A log is a power.
ln(e²) asks: e to what power is e²?
a log is a power
e to the power what is e²?
e? = e2
2 Find the power
It is already e to a power: the power is 2.
ln and e undo each other.
ln and e undo each other
So the power is 2.
e2 = e2
So ln(e²) = 2.
ln(e2) = 2
Let's look back.
First: what the log asks.
Last: find the power.
Answer
ln(e2) = 2