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Write the expression below as a single logarithm in simplest form. log_(b)10+log_(b)8 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newlinelog⁡b10+log⁡b8 \log _{b} 10+\log _{b} 8 \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⁡b10+log⁡b8 \log _{b} 10+\log _{b} 8 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to combine the logarithms.\newlineThe given expression is 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 the logarithm of the product of their arguments.\newlineProduct Property: log⁡b(M)+log⁡b(N)=log⁡b(M⋅N)\log_b (M) + \log_b (N) = \log_b (M \cdot N)
  2. Apply Property: Apply the product property to combine log⁡b10\log_{b}10 and log⁡b8\log_{b}8. Using the product property, we can write: log⁡b10+log⁡b8=log⁡b(10×8)\log_{b}10 + \log_{b}8 = \log_{b}(10 \times 8)
  3. Calculate Product: Calculate the product inside the logarithm.\newlineCalculate the product of 1010 and 88:\newline10×8=8010 \times 8 = 80
  4. Write Final Expression: Write the final expression as a single logarithm.\newlineThe final expression is:\newlinelog⁡b(80)\log_{b}(80)

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