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log_(3)81

log⁡381 \log _{3} 81

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Q. log⁡381 \log _{3} 81
  1. Rewrite as power of 33: Rewrite 8181 as a power of 33.81=3×3×3×381 = 3 \times 3 \times 3 \times 381=3481 = 3^4
  2. Evaluate log⁡334\log_3 3^4: We found: 81=3481 = 3^4\newlinelog⁡381\log_3 81 becomes log⁡334\log_3 3^4.\newlineEvaluate log⁡334\log_3 3^4.\newlineWhen the base of the logarithm matches the base of the exponent, the logarithm equals the exponent.\newlinelog⁡334=4\log_3 3^4 = 4

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