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Condense the logarithm g log c+5log q Answer: log(◻)

Condense the logarithm\newlineglog⁡c+5log⁡q g \log c+5 \log q \newlineAnswer: log⁡(□) \log (\square)

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Quotient property of logarithmsright chevron icon

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Q. Condense the logarithm\newlineglog⁡c+5log⁡q g \log c+5 \log q \newlineAnswer: log⁡(□) \log (\square)
  1. Identify Properties: Identify the properties used to condense the logarithmic expression.\newlineThe expression glog⁡c+5log⁡qg \log c + 5 \log q can be condensed using the power property of logarithms, which states that n⋅log⁡b(x)=log⁡b(xn)n \cdot \log_b(x) = \log_b(x^n).
  2. Apply Power Property: Apply the power property to each term.\newlineFor the first term, glog⁡cg \log c, we can write it as log⁡(cg)\log(c^g).\newlineFor the second term, 5log⁡q5 \log q, we can write it as log⁡(q5)\log(q^5).
  3. Combine Using Product Property: Combine the two logarithms into a single logarithm using the product property.\newlineThe product property of logarithms states that log⁡b(x)+log⁡b(y)=log⁡b(xy)\log_b(x) + \log_b(y) = \log_b(xy).\newlineTherefore, log⁡(cg)+log⁡(q5)\log(c^g) + \log(q^5) can be combined into log⁡(cg⋅q5)\log(c^g \cdot q^5).
  4. Write Final Expression: Write the final condensed logarithmic expression.\newlineThe final expression is log⁡(cg⋅q5)\log(c^g \cdot q^5).

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