# What is the domain and range of y=ln(2x-12)?

${D}_{y} = \left\{x \in \mathbb{R} : x > 6\right\} , {R}_{y} = \mathbb{R}$
On the real plane, we know that $\ln u$ is only defined for $u > 0$. So letting $u = 2 x - 12 , \ln \left(2 x - 12\right)$ is only defined for $2 x - 12 > 0 \Rightarrow x > 6$.
We also know that the range of any $\ln u$ is always the real numbers.
$\therefore {D}_{y} = \left\{x \in \mathbb{R} : x > 6\right\} , {R}_{y} = \mathbb{R}$