$\begin{array} { l }\log_{ 10 }({ 3x-21 }),\\3x-21\end{array}$
The domain of a logarithmic function are all values of $x$ for which the argument is positive$\begin{array} { l }x > 7,\\3x-21\end{array}$
The domain of a linear function is the set of all real numbers$\begin{array} { l }x > 7,\\x \in ℝ\end{array}$
Find the intersection$\begin{align*}&x \in \langle7, +\infty\rangle \\&\begin{array} { l }x > 7\end{array}\end{align*}$