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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.

Learn how to find the domain of the logarithmic function y = log(2 - 6x). This problem covers algebraic concepts and the domain property of logarithmic functions. Suitable for high school students in Grades 9-12.

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