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