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Write the expression below as a single logarithm in simplest form. 2log_(b)4 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newline2log⁡b4 2 \log _{b} 4 \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⁡b4 2 \log _{b} 4 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Question Prompt: Question Prompt: Write the expression 2log⁡b(4)2\log_b(4) 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⁡b(4)2\log_b(4) as log⁡b(42)\log_b(4^2).
  4. Calculate Exponent: Calculate the exponent. 424^2 equals 1616. So, log⁡b(42)\log_b(4^2) becomes log⁡b(16)\log_b(16).
  5. Write Final Answer: Write the final answer.\newlineThe expression 2log⁡b(4)2\log_b(4) as a single logarithm in simplest form is log⁡b(16)\log_b(16).

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