Find the Domain f(x) = log of x-3+5

$f (x) = \log (x - 3) + 5$

Set the argument in $\log (x - 3)$ greater than $0$ to find where the expression is defined.

$x - 3 > 0$

Add $3$ to both sides of the inequality.

$x > 3$

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

Interval Notation:

$(3, \infty)$

Set-Builder Notation:

${x | x > 3}$