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What is the value of log_(7)49 ? Answer:

Evalute.\newlinelog⁡749 \log _{7} 49 \newlineWrite your answer in simplest form.

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Full solution

Q. Evalute.\newlinelog⁡749 \log _{7} 49 \newlineWrite your answer in simplest form.
  1. Identify Relationship: Identify the relationship between the base of the logarithm and the number inside the logarithm.\newlineWe know that 4949 is a power of 77, specifically 727^2.
  2. Apply Definition: Apply the definition of a logarithm.\newlineThe logarithm log⁡749\log_{7} 49 asks for the exponent to which 77 must be raised to get 4949.\newlineSince 72=497^2 = 49, log⁡749\log_{7} 49 is equal to 22.

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