Step by step
The question
Question: work out ln(e⁴).
ln(e4)
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(e⁴) asks: e to what power is e⁴?
a log is a power
e to the power what is e⁴?
e? = e4
2 Find the power
It is already e to a power: the power is 4.
ln and e undo each other.
ln and e undo each other
So the power is 4.
e4 = e4
So ln(e⁴) = 4.
ln(e4) = 4
Let's look back.
First: what the log asks.
Last: find the power.
Answer
ln(e4) = 4