The exponential function is defined as a function of the form:

\[ y = e^x \quad \text{with} \quad x : \forall x \in \mathbb{R}\]

  • Domain: \(\mathbb{R} \)
  • Range: \(y \in \mathbb{R} : y > 0\)

The logarithmic function is defined as a function of the form:

\[ y = \log{_a}x \quad \text{with} \quad a \gt 0 \quad a \neq 1 \quad \forall x \in \mathbb{R}^+\]

  • Domain: \(x \in \mathbb{R}^+ \)
  • Range: \(\mathbb{R}\)