Answer
$$D = \left( {0,\infty } \right),{\text{ }}R = \left( { - \infty ,\infty } \right)$$
Work Step by Step
$$\eqalign{
& {\text{Set }}f\left( x \right) = \ln x \cr
& {\text{The domain of the function is given by all the positive real }} \cr
& {\text{numbers, then }} \cr
& {\text{Domain: }}\left\{ {\left. {x \in \Re } \right|x > 0} \right\}{\text{ or}} \cr
& D = \left( {0,\infty } \right) \cr
& {\text{The range of the function is given by all the real numbers, }} \cr
& R = \left( { - \infty ,\infty } \right) \cr} $$
