Evaluate the given logarithm.
$\log_77^{0.3}$

• A. 1.79
• B. 7
• C. 1
• D. 0.3

Answer: (D)

Verified step by step guidance

1. Understand the problem: We need to evaluate the logarithm \( \log_7 7^{0.3} \). This is a logarithmic expression where the base is 7 and the argument is \( 7^{0.3} \).
2. Recall the logarithmic identity: \( \log_b b^x = x \). This identity states that the logarithm of a base raised to an exponent is equal to the exponent itself.
3. Apply the identity: In our problem, the base \( b \) is 7, and the exponent \( x \) is 0.3. Therefore, using the identity, \( \log_7 7^{0.3} = 0.3 \).
4. Verify the understanding: The logarithm \( \log_7 7^{0.3} \) simplifies directly to 0.3 because the base and the argument are the same, and the exponent is 0.3.
5. Conclude the solution: The value of the logarithm \( \log_7 7^{0.3} \) is 0.3, as expected from the properties of logarithms.