Chapter 1 - Functions - 1.3 Inverse, Exponential, and Logarithmic Functions - 1.3 Exercises - Page 35: 9

Domain: $(0,\infty)$ Range: $(-\infty,\infty)$

Because the range of $b^{x}$ is $(0,\infty)$ the domain of $log_{b}x$ is $(0,\infty)$. The domain of $b^{x}$ is $(-\infty,\infty)$ which implies the range of $log_{b}x$ is $(-\infty,\infty)$.