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Condense the logarithm log d-7log k Answer: log(◻)

Condense the logarithm\newlinelog⁡d−7log⁡k \log d-7 \log k \newlineAnswer: log⁡(□) \log (\square)

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Q. Condense the logarithm\newlinelog⁡d−7log⁡k \log d-7 \log k \newlineAnswer: log⁡(□) \log (\square)
  1. Rewrite second term: We are given the expression log⁡(d)−7log⁡(k)\log(d) - 7\log(k) and we need to condense it into a single logarithm.\newlineAccording to the logarithm power rule, log⁡b(an)=nlog⁡b(a)\log_b(a^n) = n\log_b(a), we can rewrite the second term as a logarithm of a power.\newlinelog⁡(d)−7log⁡(k)=log⁡(d)−log⁡(k7)\log(d) - 7\log(k) = \log(d) - \log(k^7)
  2. Combine logarithms: Now, we can use the logarithm subtraction rule, which states that log⁡b(a)−log⁡b(c)=log⁡b(ac)\log_b(a) - \log_b(c) = \log_b(\frac{a}{c}), to combine the two logarithms into one.\newlinelog⁡(d)−log⁡(k7)=log⁡(dk7)\log(d) - \log(k^7) = \log(\frac{d}{k^7})

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