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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.

Write the following as a single logarithm. Assume all variables are positive: log2(4) + 2 log2(y)

Explore how to combine the expression log2(4) + 2 log2(y) into a single logarithm. This example covers logarithmic properties such as the power and product rules. Ideal for high school students studying algebra and logarithmic expressions.

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