Find the Domain g(x) = log of x-1

$g (x) = \log (x - 1)$

Set the argument in $\log (x - 1)$ greater than $0$ to find where the expression is defined.

$x - 1 > 0$

Add $1$ to both sides of the inequality.

$x > 1$

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(1, \infty)$

Set-Builder Notation:

${x | x > 1}$