Question

5=

• A. \(7^{log_{12}5}\)
• B. \(7^{log_{5}7}\)
• C. \(7^{log_{7}5}\)
• D. None

Answer 1

The Correct Option is C

To solve the problem, we need to find the correct representation for the expression \( 5 = 7^{\log_7 5} \).

1. Understanding Logarithmic Properties:
We can use the property of logarithms which states:
\[ a^{\log_a b} = b \] This property implies that \( 7^{\log_7 5} = 5 \), because the base and the logarithm's base are the same.

2. Verifying the Options:
The given equation \( 5 = 7^{\log_7 5} \) corresponds exactly to Option (3):
\[ 7^{\log_7 5} \]

Final Answer:
The correct option is Option C: \( 7^{\log_7 5} \).