Find the domain of the following function.
\[
f(x)=\log _{5}(x-6)
\]
The domain is (Type your answer in interval notation.)
Answer
\(\boxed{\text{The domain of the function is }(6, \infty)}\).
Step 1 ：The function given is \(f(x)=\log _{5}(x-6)\).
Step 2 ：The domain of a logarithmic function is the set of all real numbers for which the argument of the logarithm is greater than zero. This is because the logarithm of a negative number or zero is undefined.
Step 3 ：Therefore, we need to solve the inequality \(x-6 > 0\) to find the domain of the function.
Step 4 ：The solution to the inequality \(x - 6 > 0\) is \(x > 6\).
Step 5 ：This means that the domain of the function \(f(x) = \log_{5}(x - 6)\) is all real numbers greater than 6.
Step 6 ：\(\boxed{\text{The domain of the function is }(6, \infty)}\).
