**Simplify the expression.**

4log4(*x*5 - 7)

Group of answer choices

-7

*x*5

*x*5 - 7

5

The given expression is:  

\[
4 \log_4 (x^5 - 7)
\]

### Step 1: Apply Logarithm Properties  
One key logarithm property states that:  

\[
a \log_b C = \log_b C^a
\]

Applying this property:

\[
4 \log_4 (x^5 - 7) = \log_4 (x^5 - 7)^4
\]

### Step 2: Convert to Exponential Form  
We now rewrite it in exponential form:  

\[
\log_4 (x^5 - 7)^4 = (x^5 - 7)^4
\]

### Step 3: Analyze Answer Choices  
From the answer choices, the closest matching term is:

\[
x^5 - 7
\]

Thus, the simplified expression is:

\[
\mathbf{x^5 - 7}
\]

### **Final Answer:**
\[
\mathbf{x^5 - 7}
\]

Would you like a breakdown of logarithmic properties? Here are some related questions:

1. What are the main properties of logarithms?
2. How do you convert a logarithmic equation to exponential form?
3. What happens when the logarithm base and coefficient match?
4. How do you simplify expressions with logarithms raised to a power?
5. What are common mistakes when working with logarithmic expressions?

**Tip:** Always check if a logarithmic coefficient can be rewritten using exponent rules!

Simplify the expression.

4log4(x^5 - 7)

Group of answer choices:
-7
x^5
x^5 - 7
5

Learn how to simplify the logarithmic expression 4log4(x^5 - 7) step by step. This problem covers key logarithmic properties such as the power rule and exponential conversion, making it suitable for students in Grades 9-12.

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