To expand the logarithm $\log 6x^3$ using the properties of logarithms and express the final answer in terms of $\log x$, we will apply the following properties:

1. Product Rule: $\log(ab) = \log a + \log b$
2. Power Rule: $\log(a^b) = b \cdot \log a$

Let's expand the expression step-by-step:

1. Start with the given expression: $\log 6x^3$

2. Apply the Product Rule to separate the logarithm: $\log 6x^3 = \log 6 + \log x^3$

3. Apply the Power Rule to the term $\log x^3$: $\log x^3 = 3 \cdot \log x$

   Substituting this back into the expression gives: $\log 6x^3 = \log 6 + 3 \cdot \log x$

4. Since the problem asks for the answer in terms of $\log x$, we can express the answer as: $\log 6x^3 = \log 6 + 3 \log x$

So, the fully expanded expression in terms of $\log x$ is: $\boxed{\log 6 + 3 \log x}$

If you have any questions or want more details, feel free to ask!

Related Questions:

1. How do you apply the properties of logarithms to simplify expressions?
2. What are some common applications of logarithms in real-world scenarios?
3. How does the base of a logarithm affect its properties?
4. What is the change of base formula for logarithms, and how is it used?
5. How can logarithmic equations be solved for a specific variable?

Tip: When expanding or condensing logarithms, always look for products, quotients, or powers that can be separated using the properties of logarithms.