Question

How do you simplify `ln (1/e^3)`?

Answer 1

`ln(1/e^(3))=ln(e^(-3))=-3`.

Explanation:

Since `ln(x)` and `e^{x}` are inverse functions, `ln(e^{x})=x` for all values of `x`.

Since `1/e^{3}=e^{-3}` by definition of negative exponents, it follows that `ln(1/e^(3))=ln(e^(-3))=-3`.

You could also note that `ln(1/e^{3})=ln(1)-ln(e^{3})=0-3=-3` since `ln(A/B)=ln(A)-ln(B)` and `ln(1)=0`.