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Condense the logarithm. Assume all expressions exist and are well-defined.\newlinelog⁡a5+log⁡a3\log_a 5 + \log_a 3

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Full solution

Q. Condense the logarithm. Assume all expressions exist and are well-defined.\newlinelog⁡a5+log⁡a3\log_a 5 + \log_a 3
  1. Identify Property: Identify the property of logarithm used to condense log⁡a5+log⁡a3\log_a 5 + \log_a 3.\newlineSince these logarithms have the same base, we can apply the product rule to condense the logarithms:
  2. Apply Sum Property: Apply the product property to condense log⁡a5+log⁡a3\log_a 5 + \log_a 3.\newline log⁡bP+log⁡bQ=log⁡b(PQ)\log_b P + \log_b Q = \log_b (PQ)\newlinelog⁡a5+log⁡a3=log⁡a(5⋅3)\log_a 5 + \log_a 3 = \log_a (5 \cdot 3)
  3. Simplify Expression: Simplify the expression inside the logarithm.\newlinelog⁡a(5⋅3)=log⁡a15\log_a (5 \cdot 3) = \log_a 15

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