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Condense the logarithm 2log a-8log b Answer: log(◻)

Condense the logarithm\newline2log⁡a−8log⁡b 2 \log a-8 \log b \newlineAnswer: log⁡(□) \log (\square)

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Q. Condense the logarithm\newline2log⁡a−8log⁡b 2 \log a-8 \log b \newlineAnswer: log⁡(□) \log (\square)
  1. Apply power rule: We apply the power rule to each term: 2log⁡a2\log a becomes log⁡(a2)\log(a^2) and 8log⁡b8\log b becomes log⁡(b8)\log(b^8). log⁡(a2)−log⁡(b8)\log(a^2) - \log(b^8)
  2. Use quotient rule: Now we use the quotient rule of logarithms, which states that log⁡b(x)−log⁡b(y)=log⁡b(xy)\log_b(x) - \log_b(y) = \log_b\left(\frac{x}{y}\right), to combine the two logarithms into a single logarithm.\newlinelog⁡(a2b8)\log\left(\frac{a^2}{b^8}\right)
  3. Condense logarithm expression: We have successfully condensed the logarithm expression without any mathematical errors.

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