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Condense the logarithm log d+2log q Answer: log(◻)

Condense the logarithm\newlinelog⁡d+2log⁡q \log d+2 \log q \newlineAnswer: log⁡(□) \log (\square)

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Q. Condense the logarithm\newlinelog⁡d+2log⁡q \log d+2 \log q \newlineAnswer: log⁡(□) \log (\square)
  1. Apply Logarithm Power Rule: We are given the expression log⁡d+2log⁡q\log d + 2\log q and we need to condense it into a single logarithm.\newlineAccording to the logarithm power rule, which states that alog⁡b=log⁡(ba)a\log b = \log(b^a), we can rewrite 2log⁡q2\log q as log⁡(q2)\log(q^2).
  2. Apply Logarithm Product Rule: Now we have log⁡d+log⁡(q2)\log d + \log(q^2). According to the logarithm product rule, which states that log⁡a+log⁡b=log⁡(ab)\log a + \log b = \log(ab), we can combine these two logarithms into one.\newlineSo, log⁡d+log⁡(q2)\log d + \log(q^2) becomes log⁡(d⋅q2)\log(d \cdot q^2).
  3. Final Condensed Form: We have successfully condensed the logarithm expression into a single logarithm without any mathematical errors.\newlineThe final condensed form is log⁡(d⋅q2)\log(d \cdot q^{2}).

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