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The expression to condense is:

\[
3 \log_4 (16) + 2 \log_4 (64)
\]

Using the **Power Property of Logarithms**:

\[
n \log_b m = \log_b m^n
\]

We can first rewrite the terms:

1. \( 3 \log_4 (16) = \log_4 (16^3) = \log_4 (4096) \)
2. \( 2 \log_4 (64) = \log_4 (64^2) = \log_4 (4096) \)

Now that both terms have the same base and argument, we can apply the **Product Property**:

\[
\log_b m + \log_b n = \log_b (m \times n)
\]

Thus:

\[
\log_4 (4096) + \log_4 (4096) = \log_4 (4096 \times 4096) = \log_4 (4096^2)
\]

Finally:

\[
\log_4 (4096^2) = \log_4 (16777216)
\]

So, the condensed logarithmic expression is:

\[
\log_4 (16777216)
\]

Do you have any further questions, or would you like more explanation?

Here are 5 related questions:
1. How would the expression change if one term was subtracted instead of added?
2. What is the value of \( \log_4 (16777216) \)?
3. How can the Quotient Property of Logarithms be applied to different logarithmic expressions?
4. How would you condense an expression with different logarithmic bases?
5. What happens if the arguments inside the logarithms are fractions?

**Tip:** The Power Property is extremely useful for simplifying expressions where the logarithm has a coefficient!

Condense the following logarithmic expression: 3 log_4(16) + 2 log_4(64)

Learn how to condense the logarithmic expression 3 log_4(16) + 2 log_4(64) using the power and product properties of logarithms. This solution explains the steps involved, including applying the properties to simplify logarithmic terms. Suitable for students in Grades 9-11.

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