#### Answer

$(0, 2) \cup (2,\infty)$

#### Work Step by Step

First, we must find where our limiting components are defined:
$ln \ t$ is defined when $t>0$
The denominator $t-2$ is defined when $t\ne2$
Looking at these components, we can see our domain is limited to $(0, 2) \cup (2,\infty)$.