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Write the expression below as a single logarithm in simplest form. log_(b)5+log_(b)4 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newlinelog⁡b5+log⁡b4 \log _{b} 5+\log _{b} 4 \newlineAnswer: log⁡b(□) \log _{b}(\square)

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Quotient property of logarithmsright chevron icon

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Q. Write the expression below as a single logarithm in simplest form.\newlinelog⁡b5+log⁡b4 \log _{b} 5+\log _{b} 4 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to combine the logarithms.\newlineThe expression log⁡b(5)+log⁡b(4)\log_b(5) + \log_b(4) involves the sum of two logarithms with the same base bb.\newlineThe Product Property of logarithms states that the sum of two logarithms with the same base is equal to the logarithm of the product of their arguments.\newlineProduct Property: log⁡b(P)+log⁡b(Q)=log⁡b(P×Q)\log_b(P) + \log_b(Q) = \log_b(P \times Q)
  2. Apply Property: Apply the Product Property to combine log⁡b(5)\log_b(5) and log⁡b(4)\log_b(4). Using the Product Property, we can combine the two logarithms into a single logarithm by multiplying their arguments. log⁡b(5)+log⁡b(4)=log⁡b(5×4)\log_b(5) + \log_b(4) = \log_b(5 \times 4)
  3. Perform Multiplication: Perform the multiplication inside the logarithm.\newlineNow we multiply the numbers inside the logarithm to simplify the expression.\newline5×4=205 \times 4 = 20\newlineSo, log⁡b(5)+log⁡b(4)=log⁡b(20)\log_b(5) + \log_b(4) = \log_b(20)

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