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

Write the expression below as a single logarithm in simplest form.\newlinelog⁡b9−log⁡b9 \log _{b} 9-\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⁡b9−log⁡b9 \log _{b} 9-\log _{b} 9 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to combine the logarithms.\newlineThe expression log⁡b9−log⁡b9\log_{b}9 - \log_{b}9 involves the subtraction of two logarithms with the same base and the same argument.\newlineThe property that applies here is that the logarithm of any number minus itself is zero.\newlineCalculation: log⁡b9−log⁡b9=0\log_{b}9 - \log_{b}9 = 0
  2. Apply Property: Write the expression as a single logarithm.\newlineSince the result of the subtraction is zero, the expression as a single logarithm is simply the logarithm of 11, because the logarithm of 11 to any base is zero.\newlineCalculation: log⁡b(1)=0\log_{b}(1) = 0

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