Answer
$f(x)=\dfrac{\ln x}{x-3}$ is continuous for every positive number, except at $x=3$.
Work Step by Step
Given: $f(x)=\dfrac{\ln x}{x-3}$
As we can see that the $x$ in the denominator must be greater than zero and $x \ne 3$ .
The fraction function is continuous for every positive number, except for where it is undefined. So, $f(x)=\dfrac{\ln x}{x-3}$ is continuous for every positive number, except at $x=3$.
