Question

How do you simplify `Ln e^3`?

Answer 1

`ln(e^3)=3`

Explanation:

By definition, `log_a(x)` is the value such that `a^(log_a(x)) = x`
From this, it should be clear that for any valid `a` and `b`, `log_a(a^b)=b`, as `log_a(a^b)` is the value such that `a^(log_a(a^b))=a^b`.

As the natural logarithm `ln` is just another way of writing the base-`e` logarithm `log_e`, we have

`ln(e^3) = log_e(e^3) = 3`