It seems like you're working with logarithmic and algebraic terms. Let's break it down:

1. **log₄(x⁹ y⁴ z⁵)** can be simplified using the logarithmic property that states:  
   \[ \log_b (a \cdot b \cdot c) = \log_b a + \log_b b + \log_b c \]

2. Apply this property to your expression:  
   \[ \log_4(x^9 y^4 z^5) = \log_4(x^9) + \log_4(y^4) + \log_4(z^5) \]

3. Now, use the logarithmic power rule:  
   \[ \log_b (a^n) = n \cdot \log_b a \]

4. Applying this rule gives:  
   \[ 9 \cdot \log_4 x + 4 \cdot \log_4 y + 5 \cdot \log_4 z \]

So the simplified expression is:
\[
9 \cdot \log_4 x + 4 \cdot \log_4 y + 5 \cdot \log_4 z
\]

Would you like more details or clarifications?

Here are 5 related questions to expand on this concept:
1. What are the properties of logarithms that help simplify expressions?
2. How do you handle logarithms with different bases?
3. What is the change of base formula for logarithms?
4. How do logarithmic equations relate to exponential equations?
5. Can logarithms have negative arguments or results?

**Tip**: Always remember to apply the power rule of logarithms when simplifying terms involving exponents.

Learn how to simplify the logarithmic expression log₄(x⁹ y⁴ z⁵) using properties of logarithms, such as the product property and power rule. This solution includes step-by-step explanations for students in Grades 10-12.

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