What is the domain of the function f(x)=-5/2log(x-3)+2 in interval notation?

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 \(\boxed{(3, \infty)}\).