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Write the expression below as a single logarithm in simplest form. 3log_(b)4 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newline3log⁡b4 3 \log _{b} 4 \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⁡b4 3 \log _{b} 4 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to rewrite the expression 3log⁡b43\log_{b}4 as a single logarithm.\newlineThe Power Property of logarithms states that nlog⁡b(A)=log⁡b(An)n\log_b(A) = \log_b(A^n), where nn is a coefficient, log⁡b\log_b is the logarithm base bb, and AA is the argument of the logarithm.
  2. Apply Power Property: Apply the Power Property to the given expression.\newlineUsing the Power Property, we can rewrite 3log⁡b43\log_{b}4 as log⁡b(43)\log_{b}(4^{3}).
  3. Calculate Value: Calculate the value of 434^3. \newline43=4×4×4=644^3 = 4 \times 4 \times 4 = 64
  4. Write Final Expression: Write the final expression as a single logarithm.\newlineThe expression 3log⁡b43\log_{b}4 is equivalent to log⁡b(64)\log_{b}(64).

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