Question

Find the domains of definition of the following function:
$y=\frac{1}{3-{\log }_3(x-3)}.$

Answer 1

$y=\frac{1}{3-{log}_3(x-3)}\Rightarrow {log}_3(x-3)=3\Rightarrow x-3=27\Rightarrow x=30$

For $y$ to be real an defined.

Therefore domain of $y$ is $x>3$ and $x\ne 30.$

Therefore, $x\in (3,\infty )-\left\{30\right\}x\in (3,30)\cup (30,\infty ).$