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

Write the expression below as a single logarithm in simplest form.\newlinelog⁡b10−log⁡b10 \log _{b} 10-\log _{b} 10 \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⁡b10 \log _{b} 10-\log _{b} 10 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to combine the logarithms.\newlineThe expression given is log⁡b(10)−log⁡b(10)\log_b(10) - \log_b(10), which involves the subtraction of two logarithms with the same base.\newlineThe subtraction of logarithms corresponds to the division of their arguments according to 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(10)−log⁡b(10)=log⁡b(1010)\log_b(10) - \log_b(10) = \log_b(\frac{10}{10})
  3. Simplify Argument: Simplify the argument of the logarithm.\newlineThe argument of the logarithm simplifies to:\newline1010=1\frac{10}{10} = 1\newlineSo, the expression becomes log⁡b(1)\log_b(1).
  4. Recognize Logarithm Value: Recognize the value of the logarithm of 11. The logarithm of 11 to any base is always 00 because any number raised to the power of 00 is 11. Therefore, log⁡b(1)=0\log_b(1) = 0.

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