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Write the expression below as a single logarithm in simplest form. log_(b)7+log_(b)9 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newlinelog⁡b7+log⁡b9 \log _{b} 7+\log _{b} 9 \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⁡b7+log⁡b9 \log _{b} 7+\log _{b} 9 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to combine the sum of logarithms.\newlineWhen adding two logarithms with the same base, we can use the product property of logarithms.\newlineProduct Property: log⁡b(M)+log⁡b(N)=log⁡b(M×N)\log_b (M) + \log_b (N) = \log_b (M \times N)\newlineWe will apply this property to combine log⁡b7\log_{b}7 and log⁡b9\log_{b}9 into a single logarithm.
  2. Apply Product Property: Apply the product property to combine log⁡b7\log_{b}7 and log⁡b9\log_{b}9.\newlineUsing the product property, we get:\newlinelog⁡b7+log⁡b9=log⁡b(7×9)\log_{b}7 + \log_{b}9 = \log_{b}(7 \times 9)\newlineNow, we calculate the product inside the logarithm.\newline7×9=637 \times 9 = 63\newlineSo, log⁡b7+log⁡b9=log⁡b(63)\log_{b}7 + \log_{b}9 = \log_{b}(63)

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