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Condense the logarithm 3log a+log k Answer: log(◻)

Condense the logarithm\newline3log⁡a+log⁡k 3 \log a+\log k \newlineAnswer: log⁡(□) \log (\square)

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Q. Condense the logarithm\newline3log⁡a+log⁡k 3 \log a+\log k \newlineAnswer: log⁡(□) \log (\square)
  1. Apply Logarithm Power Rule: We are given the logarithmic expression 3log⁡a+log⁡k3\log a + \log k and we need to condense it into a single logarithm.\newlineAccording to the logarithm power rule, which states that n⋅log⁡b(x)=log⁡b(xn)n \cdot \log_b(x) = \log_b(x^n), we can rewrite 3log⁡a3\log a as log⁡a3\log a^3.
  2. Apply Logarithm Product Rule: Now we have log⁡a3+log⁡k\log a^3 + \log k. According to the logarithm product rule, which states that log⁡b(x)+log⁡b(y)=log⁡b(xy)\log_b(x) + \log_b(y) = \log_b(xy), we can combine these two logarithms into one.\newlineSo, log⁡a3+log⁡k\log a^3 + \log k becomes log⁡(a3⋅k)\log(a^3 \cdot k).
  3. Final Condensed Form: We have successfully condensed the logarithm into a single expression without making any mathematical errors.\newlineThe final condensed form is log⁡(a3⋅k)\log(a^3 \cdot k).

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