Step by step
The question
Question: work out ln(e⁷).
ln(e7)
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(e⁷) asks: e to what power is e⁷?
a log is a power
e to the power what is e⁷?
e? = e7
2 Find the power
It is already e to a power: the power is 7.
ln and e undo each other.
ln and e undo each other
So the power is 7.
e7 = e7
So ln(e⁷) = 7.
ln(e7) = 7
Let's look back.
First: what the log asks.
Last: find the power.
Answer
ln(e7) = 7