If `log_b` x=p and `log_b` y=q, then `log_b` xy=

Options

A. pq
B. p+q
C. `p/q`
D. p-q

Explanation

To solve the problem, we need to find the value of \( \log_b (xy) \) given that \( \log_b x = p \) and \( \log_b y = q \).

### Step-by-Step Solution:

1. **Understanding the Logarithm Property**:
We start with the property of logarithms that states:
\[ \log_b (mn) = \log_b m + \log_b n \]
This property allows us to break down the logarithm of a product into the sum of the logarithms.

2. **Applying the Property**:
In our case, we want to find \( \log_b (xy) \). We can apply the property of logarithms:
\[ \log_b (xy) = \log_b x + \log_b y \]

3. **Substituting Known Values**:
We know from the problem statement that:
\[ \log_b x = p \quad \text{and} \quad \log_b y = q \]
Substituting these values into the equation gives:
\[ \log_b (xy) = p + q \]

4. **Final Result**:
Therefore, the value of \( \log_b (xy) \) is:
\[ \log_b (xy) = p + q \]

### Conclusion:
The final answer is:
\[ \log_b (xy) = p + q \]