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

Write the expression below as a single logarithm in simplest form.\newline4log⁡b2 4 \log _{b} 2 \newlineAnswer: log⁡b(□) \log _{b}(\square)

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Quotient property of logarithmsright chevron icon

Full solution

Q. Write the expression below as a single logarithm in simplest form.\newline4log⁡b2 4 \log _{b} 2 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to expand 4log⁡b24\log_{b}2. The expression 4log⁡b24\log_{b}2 involves a constant multiple of a logarithm. The Power Property of logarithms can be used to rewrite a constant multiple of a logarithm as a single logarithm.\newlinePower Property: k⋅log⁡b(P)=log⁡b(Pk)k \cdot \log_{b} (P) = \log_{b} (P^{k})
  2. Apply Power Property: Apply the Power Property to rewrite 4log⁡b24\log_{b}2 as a single logarithm.\newlineUsing the Power Property, we can rewrite 4log⁡b24\log_{b}2 as log⁡b(24)\log_{b}(2^4).\newlineCalculation: 24=162^4 = 16
  3. Rewrite as Single Logarithm: Write the final expression as a single logarithm.\newlineThe final expression is log⁡b(16)\log_{b}(16).

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