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log_(3)729=

log⁡3729= \log _{3} 729=

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Full solution

Q. log⁡3729= \log _{3} 729=
  1. Identify Relationship: Identify the relationship between the base of the logarithm and the number.\newlineWe know that 729729 is a power of 33, specifically 36=7293^6 = 729.
  2. Apply Definition of Logarithm: Apply the definition of a logarithm.\newlineThe logarithm log⁡3729\log_{3}729 asks for the exponent to which the base 33 must be raised to produce 729729.\newlineSince 36=7293^6 = 729, log⁡3729=6\log_{3}729 = 6.
  3. Check for Errors: Check for any mathematical errors.\newlineWe have correctly identified that 729729 is 363^6 and applied the definition of a logarithm without any errors.

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