Answer
Domain:$\quad (-\infty, 7) \cup (7, \infty)$
or, $\{x\in \mathbb{R}\ |\ x\neq 7\}$
Work Step by Step
Logarithmic functions are defined for positive arguments only.
The argument here is $(x-7)^{2}$, which is never negative. The only problem is when it is zero.
So, the domain is all reals except $7$.
Domain:$\quad (-\infty, 7) \cup (7, \infty)$
or, $\{x\in \mathbb{R}\ |\ x\neq 7\}$
