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

Write the expression below as a single logarithm in simplest form.\newline2log⁡b5 2 \log _{b} 5 \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.\newline2log⁡b5 2 \log _{b} 5 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Property: Identify the property used to rewrite the expression 2log⁡b52\log_{b}5 as a single logarithm.\newlineThe Power Property of logarithms states that a multiple of a logarithm can be written as the logarithm of the base raised to the power of that multiple.\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 2log⁡b52\log_{b}5 as a single logarithm.\newlineUsing the Power Property, we can write 2log⁡b52\log_{b}5 as log⁡b(52)\log_{b}(5^2).
  3. Simplify Expression: Simplify the expression inside the logarithm.\newlineSimplifying 525^2 gives us 2525.\newlineSo, log⁡b(52)\log_{b}(5^2) becomes log⁡b(25)\log_{b}(25).

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