Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form. \( \log _{81} 9=\square \) Save answer Skip to next question >

To evaluate \( \log_{81} 9 \), we can use the change of base formula or rewrite the expressions as powers of the same base. Since \( 81 = 3^4 \) and \( 9 = 3^2 \), we can express the logarithm as: \[ \log_{81} 9 = \log_{3^4} 3^2 \] Using the change of base formula, this gives us: \[ \log_{81} 9 = \frac{\log_3 3^2}{\log_3 3^4} \] This simplifies to: \[ \log_{81} 9 = \frac{2}{4} = \frac{1}{2} \] Thus, the answer is \( \frac{1}{2} \).