The problem asks for the value of $\log 18$ in terms of $p$ and $q$, given that $\log 2 = p$ and $\log 3 = q$.

Solution:

We know: $\log 18 = \log (2 \cdot 3^2)$

Using the logarithmic property $\log(ab) = \log a + \log b$, we have: $\log 18 = \log 2 + \log(3^2)$

Using the property $\log(a^b) = b \log a$, this becomes: $\log 18 = \log 2 + 2 \log 3$

Substitute $\log 2 = p$ and $\log 3 = q$: $\log 18 = p + 2q$

Answer:

The correct option is C. $p + 2q$.

Would you like a breakdown of logarithmic rules or further clarifications?

Here are some questions to extend your understanding:

1. How would you calculate $\log(2^3 \cdot 5)$ in terms of $\log 2$ and $\log 5$?
2. What are the properties of logarithms that simplify complex expressions?
3. If $\log 2 = 0.3010$ and $\log 3 = 0.4771$, what is the approximate value of $\log 18$?
4. How can you use the change of base formula to evaluate logarithms not in base 10?
5. What is the difference between $\log a^b$ and $(\log a)^b$?

Tip: Always simplify logarithmic expressions step-by-step using properties like product, power, and quotient rules!