Find the domain of the function $f(x)=\log (3-7 x)$. Write your answer using interval notation. The domain of $f(x)$ is

Step 1 ：Find the domain of the function \(f(x)=\log (3-7 x)\). Write your answer using interval notation.

Step 2 ：The domain of a logarithmic function is the set of all real numbers for which the argument of the logarithm is positive. In this case, we need to find the values of \(x\) for which \(3-7x > 0\).

Step 3 ：Solve the inequality \(3-7x > 0\). The solution to this inequality is \(x < \frac{3}{7}\).

Step 4 ：This means that the domain of the function \(f(x)=\log (3-7 x)\) is \((-\infty, \frac{3}{7})\).

Step 5 ：Final Answer: The domain of the function \(f(x)=\log (3-7 x)\) is \(\boxed{(-\infty, \frac{3}{7})}\).