Use the power property to rewrite the log expression.
${\log }_9{5}^4$

• A. $5{\log }_{9}4$
• B. $5{\log }_{4}9$
• C. $4{\log }_{9}5$
• D. $4{\log }_{5}9$

Answer: (C)

Verified step by step guidance

1. Identify the given logarithmic expression: \(\log_9 5^4\).
2. Recall the power property of logarithms, which states that \(\log_b (a^n) = n \log_b a\).
3. Apply the power property by moving the exponent 4 in front of the logarithm: \(\log_9 5^4 = 4 \log_9 5\).
4. Write the expression with the exponent as a coefficient: \(4 \log_9 5\).
5. This is the rewritten form of the original logarithmic expression using the power property.