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!