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Write the expression below as a single logarithm in simplest form. 5log_(b)2 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newline5log⁡b2 5 \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.\newline5log⁡b2 5 \log _{b} 2 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to rewrite the expression 5log⁡b25\log_{b}2 as a single logarithm.\newlineThe Power Property of logarithms states that a coefficient can be rewritten as an exponent inside the logarithm.\newlinePower Property: a⋅log⁡b(P)=log⁡b(Pa)a \cdot \log_b (P) = \log_b (P^a)
  2. Apply Power Property: Apply the Power Property to rewrite 5log⁡b25\log_{b}2 as a single logarithm.\newlineUsing the Power Property, we can move the coefficient 55 inside the logarithm as an exponent of 22.\newlineSo, 5log⁡b25\log_{b}2 becomes log⁡b(25)\log_{b}(2^5).
  3. Calculate Value: Calculate the value of 252^5 to simplify the expression further.\newline25=2×2×2×2×2=322^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32
  4. Write Final Expression: Write the final expression as a single logarithm.\newlineThe expression 5log⁡b25\log_{b}2 is now written as log⁡b(32)\log_{b}(32).

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