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Condense the logarithm 5log b+3log r Answer: log(◻)

Condense the logarithm\newline5log⁡b+3log⁡r 5 \log b+3 \log r \newlineAnswer: log⁡(□) \log (\square)

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Quotient property of logarithmsright chevron icon

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Q. Condense the logarithm\newline5log⁡b+3log⁡r 5 \log b+3 \log r \newlineAnswer: log⁡(□) \log (\square)
  1. Identify Property: Identify the property used to condense the logarithm.\newlineWhen you have a coefficient in front of a logarithm, you can use the power property to move the coefficient inside the logarithm as an exponent of the argument.\newlinePower Property: n⋅log⁡b(P)=log⁡b(Pn)n \cdot \log_b (P) = \log_b (P^n)
  2. Apply Power Property: Apply the power property to each term.\newlineFor the first term, 5log⁡b5\log b, we apply the power property to get log⁡(b5)\log(b^5).\newlineFor the second term, 3log⁡r3\log r, we apply the power property to get log⁡(r3)\log(r^3).
  3. Combine Using Product Property: Combine the two logarithms into one using the product property.\newlineProduct Property: log⁡bP+log⁡bQ=log⁡b(P×Q)\log_b P + \log_b Q = \log_b (P \times Q)\newlineCombine log⁡(b5)\log(b^5) and log⁡(r3)\log(r^3) using the product property to get log⁡(b5×r3)\log(b^5 \times r^3).

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