Exponential function (Statistics)

has usedul properties like so;

$$e^0 = 1$$

$$e^x \Rightarrow 0 as x \Rightarrow -\infty$$

exp is an increasing function

$$e^{x+y} = e^x \times e^y$$

log functions
$$a \in \mathbb{R}, log x^a = a log x$$

$$log(xy) = log(x) + log(y)$$

$$log(\frac{x}{y})=log x - log y$$

$$log(\frac{1}{x})= - log x$$