To solve the problem, we need to simplify $3 + \log_2 x$ into a single logarithmic expression.

Step-by-Step Solution:

1. Recall the logarithmic rule: $a + \log_b x = \log_b(b^a \cdot x)$ Here, $a$ represents a constant (in this case, $3$).

2. Rewrite $3$ as a logarithm: Since $3 = \log_2(2^3)$, we can substitute this into the expression: $3 + \log_2 x = \log_2(2^3) + \log_2 x$

3. Apply the logarithmic addition rule: $\log_b(A) + \log_b(B) = \log_b(A \cdot B)$ Using this, we combine the terms: $\log_2(2^3) + \log_2 x = \log_2(2^3 \cdot x) = \log_2(8x)$

4. Final Answer: $\boxed{\log_2(8x)}$

This matches option C in the provided question.

Let me know if you'd like more details or clarification!
Here are 5 related questions to expand your understanding:

1. How would the expression change if the base of the logarithm were $10$ instead of $2$?
2. What if the constant $3$ were replaced with $4$? What would the result be?
3. Can $3 + \log_2 x$ be simplified without using logarithmic rules?
4. What is the result of $\log_2(8x)$ if $x = 1$?
5. How does the logarithmic rule $\log_b(A) + \log_b(B) = \log_b(A \cdot B)$ apply to solving real-world problems?

Tip: Always rewrite constants in terms of logarithms of the same base for easier simplification!