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Write the expression below as a single logarithm in simplest form. 2log_(b)8 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newline2log⁡b8 2 \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.\newline2log⁡b8 2 \log _{b} 8 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Question Prompt: Question Prompt: Write the expression 2log⁡b82\log_{b}8 as a single logarithm in simplest form.
  2. Identify Property: Identify the property used to write the expression as a single logarithm.\newlineThe Power Property of logarithms states that a coefficient in front of a logarithm can be rewritten as an exponent inside the logarithm. The property is: alog⁡b(x)=log⁡b(xa)a\log_b(x) = \log_b(x^a).
  3. Apply Power Property: Apply the Power Property to the given expression.\newlineUsing the Power Property, we can rewrite 2log⁡b82\log_{b}8 as log⁡b(82)\log_{b}(8^2).
  4. Calculate Exponent: Calculate the exponent. 828^2 equals 6464.
  5. Write Final Expression: Write the final expression.\newlineThe expression 2log⁡b82\log_{b}8 can be written as log⁡b(64)\log_{b}(64).

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