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Condense the logarithm x log b+7log k Answer: log(◻)

Condense the logarithm\newlinexlog⁡b+7log⁡k x \log b+7 \log k \newlineAnswer: log⁡(□) \log (\square)

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Q. Condense the logarithm\newlinexlog⁡b+7log⁡k x \log b+7 \log k \newlineAnswer: log⁡(□) \log (\square)
  1. Identify Properties: Identify the properties of logarithms that can be used to condense the expression.\newlineThe expression xlog⁡b+7log⁡kx \log b + 7 \log k can be condensed using the power property of logarithms, which states that n⋅log⁡b(a)=log⁡b(an)n \cdot \log_b(a) = \log_b(a^n).
  2. Apply Power Property: Apply the power property to each term in the expression.\newlineFor the first term, xlog⁡bx \log b, we can write it as log⁡(bx)\log(b^x).\newlineFor the second term, 7log⁡k7 \log k, we can write it as log⁡(k7)\log(k^7).
  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(u)+log⁡b(v)=log⁡b(uv)\log_b(u) + \log_b(v) = \log_b(uv).\newlineTherefore, we can combine the two terms to get log⁡(bx⋅k7)\log(b^x \cdot k^7).

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