Final answer:
The domain of the logarithmic function f(x)=log_(3)(x-6) is x ≥ 6.
Step-by-step explanation:
The domain of a logarithmic function is the set of all real numbers for which the function is defined. In this case, the logarithmic function is f(x) = log3(x-6).
To determine the domain, we need to find the values of x that make the expression inside the logarithm non-negative.
x-6 ≥ 0
x ≥ 6
Therefore, the domain of the logarithmic function is x ≥ 6.