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Simplify each logarithm \newlinelog⁡37+log⁡38\log_{3}7+\log_{3}8

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Full solution

Q. Simplify each logarithm \newlinelog⁡37+log⁡38\log_{3}7+\log_{3}8
  1. Identify Property: Identify the property of logarithms to simplify the sum.\newlineUsing the property that log⁡b(a)+log⁡b(b)=log⁡b(ab)\log_b(a) + \log_b(b) = \log_b(ab), we can combine the logarithms.\newlinelog⁡37+log⁡38=log⁡3(7×8)\log_{3}7 + \log_{3}8 = \log_{3}(7\times8)
  2. Combine Logarithms: Calculate the product inside the logarithm.\newline7×8=567 \times 8 = 56\newlineSo, log⁡37+log⁡38=log⁡356\log_{3}7 + \log_{3}8 = \log_{3}56

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