What's the 54th problems first problem solution and answer

The first problem in **54** involves the following expression:

\[
\log_2 3 + \log_2 5
\]

### Step-by-step solution:

1. **Apply the Product Rule of Logarithms:**
   The product rule states:
   \[
   \log_b x + \log_b y = \log_b (x \cdot y)
   \]
   In this case:
   \[
   \log_2 3 + \log_2 5 = \log_2 (3 \times 5)
   \]

2. **Simplify the expression:**
   Multiply the numbers inside the logarithm:
   \[
   \log_2 (3 \times 5) = \log_2 15
   \]

Thus, the solution is:
\[
\log_2 15
\]

### Final Answer:
\[
\log_2 15
\]

Would you like me to explain another problem or need further clarification on logarithmic properties?

### Related Questions:
1. What is the solution for \( \log_b x + \log_b y \) if \( b = 10 \), \( x = 2 \), and \( y = 8 \)?
2. How can the logarithm of a product, like \( \log_b (xy) \), be split into simpler parts?
3. Can you convert \( \log_2 15 \) into a different logarithmic base?
4. What is the inverse function of \( \log_b x \)?
5. How do you solve logarithmic equations using the product rule?

### Tip:
Always check if logarithmic terms can be combined using the product or quotient rule to simplify the expression quickly!

Learn how to solve the logarithmic expression log base 2 of 3 plus log base 2 of 5 with a step-by-step solution. This problem covers logarithmic properties and the product rule of logarithms. Suitable for high school students.

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