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Condense the logarithm. Assume all expressions exist and are well-defined.\newlinelog⁡29−log⁡24\log_2 9 - \log_2 4

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Full solution

Q. Condense the logarithm. Assume all expressions exist and are well-defined.\newlinelog⁡29−log⁡24\log_2 9 - \log_2 4
  1. Identify Property: Identify the property of logarithm used to condense log⁡29−log⁡24\log_2 9 - \log_2 4.\newlineSince these logarithms have the same base, we can apply the quotient rule to condense the logarithms:
  2. Use Quotient Property: Use the quotient property of logarithms: log⁡b(P)−log⁡b(Q)=log⁡b(PQ)\log_b (P) - \log_b (Q) = \log_b \left(\frac{P}{Q}\right).
  3. Apply Quotient Property: Apply the quotient property: log⁡29−log⁡24=log⁡2(94)\log_2 9 - \log_2 4 = \log_2 \left(\frac{9}{4}\right).

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