Step 1 :Find the domain of the logarithmic function: \(f(x)=\ln (8-x)\)
Step 2 :Since the natural logarithm is only defined for positive numbers, we need to find the values of x that will make the expression inside the logarithm \((8-x)\) positive.
Step 3 :Solve the inequality: \(8-x > 0\)
Step 4 :Add x to both sides: \(8 > x\)
Step 5 :Final Answer: \(\boxed{(-\infty, 8)}\)