To find the domain of the function $y = \log(2 - 6x)$, we need to remember that the argument inside the logarithm must be positive. Specifically, the expression $2 - 6x$ must satisfy:

$2 - 6x > 0$

Solve the inequality:

$2 > 6x$

Now, divide both sides by 6: $\frac{2}{6} > x$

Simplifying: $\frac{1}{3} > x$

Thus, the domain is: $x < \frac{1}{3}$

Final answer:

The domain is $(-\infty, \frac{1}{3})$.

Would you like a detailed explanation of the steps, or do you have any questions?

Here are some related questions:

1. How do you find the domain of a logarithmic function in general?
2. What happens if the argument of a logarithmic function is zero or negative?
3. Can the base of a logarithm affect the domain of a function?
4. How can inequalities be used to find the domain of more complex functions?
5. How does the transformation of a logarithmic function (e.g., shifting) affect its domain?

Tip: Always remember to check the argument of a logarithmic function to ensure it's positive for the function to be valid.