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Write the expression below as a single logarithm in simplest form. 3log_(b)3 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newline3log⁡b3 3 \log _{b} 3 \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.\newline3log⁡b3 3 \log _{b} 3 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to rewrite the expression 3log⁡b33\log_{b}3 as a single logarithm.\newlineThe Power Property of logarithms states that nlog⁡b(x)=log⁡b(xn)n\log_{b}(x) = \log_{b}(x^n). We will use this property to rewrite the given expression.
  2. Apply Power Property: Apply the Power Property to the given expression.\newlineUsing the Power Property, we can rewrite 3log⁡b33\log_{b}3 as log⁡b(33)\log_{b}(3^3).
  3. Calculate Value: Calculate the value of 333^3. \newline33=3×3×3=273^3 = 3 \times 3 \times 3 = 27.
  4. Write Final Expression: Write the final expression as a single logarithm.\newlineThe expression 3log⁡b33\log_{b}3 is equivalent to log⁡b(27)\log_{b}(27).

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