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The problem asks to apply the power property of logarithms to the expression:

\[
\log \left( (4t - 3)^4 \right)
\]

The power property of logarithms states that:

\[
\log_b(x^n) = n \cdot \log_b(x)
\]

Applying this property to the expression:

\[
\log \left( (4t - 3)^4 \right) = 4 \cdot \log(4t - 3)
\]

Thus, the answer is:

\[
4 \cdot \log(4t - 3)
\]

Let me know if you would like further explanation or have any questions. 

Here are five related questions to consider:
1. How can you simplify the logarithmic expression \(\log(5x^3)\)?
2. What happens if you apply the power property to a logarithm with a fraction inside?
3. How do you simplify \(\log(a^n \cdot b^m)\) using logarithmic properties?
4. What is the result of applying the power property to a logarithmic expression with multiple terms?
5. How do you combine \(\log(a) + \log(b)\) into a single logarithmic expression?

Tip: Always check if the expression inside the logarithm is positive before simplifying, as logarithms are only defined for positive values.

Apply the power property of logarithms. Assume that all variable expressions represent positive real numbers. log((4t - 3)^4) = ?

Learn how to apply the power property of logarithms to simplify log((4t - 3)^4). This step-by-step explanation shows how to use the formula log_b(x^n) = n * log_b(x) and is ideal for students in Grades 9-11.

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