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Write the expression below as a single logarithm in simplest form. 2log_(b)9 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newline2log⁡b9 2 \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.\newline2log⁡b9 2 \log _{b} 9 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Question Prompt: Question Prompt: Write the expression 2log⁡b92\log_{b}9 as a single logarithm in simplest form.
  2. Identify Property: Identify the property used to write the expression as a single logarithm.\newlineThe expression 2log⁡b92\log_{b}9 involves a logarithm with a coefficient. To write this as a single logarithm, we use the power property of logarithms.\newlinePower Property: alog⁡b(P)=log⁡b(Pa)a\log_{b}(P) = \log_{b}(P^{a})
  3. Apply Power Property: Apply the power property to the given expression.\newlineUsing the power property, we can move the coefficient 22 inside the logarithm as an exponent of the argument.\newline2log⁡b9=log⁡b(92)2\log_{b}9 = \log_{b}(9^2)
  4. Calculate Exponent: Calculate the exponent.\newlineNow we calculate 929^2 to simplify the expression inside the logarithm.\newline92=819^2 = 81
  5. Write Final Expression: Write the final expression.\newlineThe expression as a single logarithm in simplest form is:\newlinelog⁡b(81)\log_{b}(81)

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