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Write the expression below as a single logarithm in simplest form. log_(b)6-log_(b)2 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newlinelog⁡b6−log⁡b2 \log _{b} 6-\log _{b} 2 \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⁡b6−log⁡b2 \log _{b} 6-\log _{b} 2 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to combine the logarithms.\newlineWe have the expression log⁡b(6)−log⁡b(2)\log_b(6) - \log_b(2), which involves the subtraction of two logarithms with the same base bb.\newlineThe property that allows us to combine these logarithms is the quotient property of logarithms.\newlineQuotient Property: log⁡b(P)−log⁡b(Q)=log⁡b(PQ)\log_b(P) - \log_b(Q) = \log_b\left(\frac{P}{Q}\right)
  2. Apply Quotient Property: Apply the quotient property to combine the logarithms.\newlineUsing the quotient property, we can write the expression as a single logarithm:\newlinelog⁡b(6)−log⁡b(2)=log⁡b(62)\log_b(6) - \log_b(2) = \log_b\left(\frac{6}{2}\right)
  3. Simplify Fraction: Simplify the fraction inside the logarithm.\newlineSimplify the fraction 62\frac{6}{2} to get 33:\newlinelog⁡b(62)=log⁡b(3)\log_b\left(\frac{6}{2}\right) = \log_b(3)
  4. Write Final Answer: Write the final answer.\newlineThe expression log⁡b(6)−log⁡b(2)\log_b(6) - \log_b(2) as a single logarithm in simplest form is log⁡b(3)\log_b(3).

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