Answer
domain: $(-\infty,1)\cup(1, \infty)$
Work Step by Step
The restriction for the domain of a logarithmic function is that its argument must be positive.
Domain: all $x$ for which $(x-1)^{2}>0$
Now, the square of a number is never negative, so the only problem is when it is 0.
domain: $x\neq 1$
In interval notation,
domain: $(-\infty,1)\cup(1, \infty)$