To combine the expression $\log_2(4) + 2\log_2(y)$ into a single logarithm, follow these steps:

1. Evaluate $\log_2(4)$: Since $4 = 2^2$, we can simplify this: $\log_2(4) = \log_2(2^2) = 2$

2. Apply the power rule to $2\log_2(y)$: The power rule states $a\log_b(c) = \log_b(c^a)$. So, we can rewrite $2\log_2(y)$ as: $2\log_2(y) = \log_2(y^2)$

3. Combine the logarithms using the addition rule: The addition rule for logarithms states that $\log_b(A) + \log_b(B) = \log_b(AB)$. Therefore, we can combine the expressions: $2 + \log_2(y^2) = \log_2(4) + \log_2(y^2) = \log_2(4y^2)$

Thus, the final expression as a single logarithm is: $\log_2(4y^2)$

Would you like further details or have any questions?

Here are some related questions:

1. How do logarithmic rules apply to solving exponential equations?
2. What is the difference between common logarithms and natural logarithms?
3. How can we expand a logarithmic expression that is already simplified?
4. What is the change of base formula for logarithms, and how is it used?
5. How do we solve equations involving multiple logarithms?

Tip: When simplifying logarithmic expressions, remember to apply the power rule and product rule to combine terms efficiently.