Step 1 :The function given is \(f(x)=-\frac{5}{2}\log(x-3)+2\).
Step 2 :The domain of a logarithmic function is the set of all real numbers for which the argument of the logarithm is positive.
Step 3 :In this case, the argument of the logarithm is \((x-3)\). Therefore, the domain of the function is the set of all real numbers x such that \(x-3 > 0\).
Step 4 :Solving this inequality will give us the domain of the function.
Step 5 :The solution to the inequality \(x-3 > 0\) is \(x > 3\).
Step 6 :This means that the domain of the function is all real numbers greater than 3.
Step 7 :In interval notation, this is represented as \((3, \infty)\).
Step 8 :Final Answer: The domain of the function \(f(x)=-\frac{5}{2}\log(x-3)+2\) in interval notation is \(\boxed{(3, \infty)}\).