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Which of the following is equivalent to log((a)/(b)). a)(log a)/(log b) b)log(a-b) c)log a-log b d)log b-log a

Which of the following is equivalent to log⁡(ab)\log\left(\frac{a}{b}\right).\newlinea) log⁡alog⁡b\frac{\log a}{\log b}\newlineb) log⁡(a−b)\log(a-b)\newlinec) log⁡a−log⁡b\log a-\log b\newlined) log⁡b−log⁡a\log b-\log a

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Quotient property of logarithmsright chevron icon

Full solution

Q. Which of the following is equivalent to log⁡(ab)\log\left(\frac{a}{b}\right).\newlinea) log⁡alog⁡b\frac{\log a}{\log b}\newlineb) log⁡(a−b)\log(a-b)\newlinec) log⁡a−log⁡b\log a-\log b\newlined) log⁡b−log⁡a\log b-\log a
  1. Identify Property: Identify the property used to expand log⁡(ab)\log\left(\frac{a}{b}\right). Using the quotient property of logarithms, which states log⁡b(PQ)=log⁡bP−log⁡bQ\log_b\left(\frac{P}{Q}\right) = \log_b P - \log_b Q.
  2. Apply Quotient Property: Apply the quotient property to log⁡(ab)\log\left(\frac{a}{b}\right).\newlinelog⁡(ab)=log⁡a−log⁡b\log\left(\frac{a}{b}\right) = \log a - \log b.
  3. Compare with Options: Compare the expanded form with the given options.\newlineThe correct form log⁡a−log⁡b\log a - \log b matches with one of the options.

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