Question
Evaluate \( \log _{3} 81 \) \( \log _{3} 81=\square \)
Ask by Summers Harrington. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \log_{3}(81) = 4 \)
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Mind Expander
To evaluate \( \log_{3} 81 \), we first express 81 as a power of 3. We know that \( 81 = 3^4 \). Therefore, we can rewrite the logarithm: \[ \log_{3} 81 = \log_{3}(3^4). \] Using the logarithmic identity \( \log_{b}(b^k) = k \), we have: \[ \log_{3}(3^4) = 4. \] Thus, \[ \log_{3} 81 = 4. \] So, \( \log_{3} 81 = \boxed{4} \).
