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To solve the problem, we are given the following information:

\[
\log 2 = a \quad \text{and} \quad \log 3 = b
\]
We are asked to find the value of \( \log 18 \) in terms of \( a \) and \( b \).

### Step 1: Express \( \log 18 \) in terms of its factors.
Since \( 18 = 2 \times 3^2 \), we can use logarithmic properties to expand \( \log 18 \):
\[
\log 18 = \log(2 \times 3^2)
\]
Using the product rule of logarithms:
\[
\log 18 = \log 2 + \log 3^2
\]
Now, apply the power rule \( \log x^n = n \log x \):
\[
\log 18 = \log 2 + 2\log 3
\]

### Step 2: Substitute \( \log 2 = a \) and \( \log 3 = b \).
\[
\log 18 = a + 2b
\]

### Step 3: Conclusion
The value of \( \log 18 \) is \( a + 2b \), which corresponds to option **A**.

Let me know if you'd like further clarification or details on any part of this solution! 

Here are five related questions you might find helpful:

1. What are the other logarithmic properties, and how are they applied?
2. How would you calculate \( \log 54 \) using the same method?
3. Can you prove the product and power rules of logarithms?
4. How do logarithms apply to exponential equations?
5. How do you solve logarithmic equations in terms of variables?

**Tip:** When working with logarithms, it's helpful to break complex expressions into simpler factors to use the basic logarithmic properties effectively.

If log 2 = a and log 3 = b, what is the value of log 18?

Solve the logarithmic problem where log 2 = a and log 3 = b to find the value of log 18. Learn the application of the product and power rules of logarithms. Suitable for Grades 10-12.

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