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Use the quotient property of logs to write as a difference of logarithms. Simplify if possible. log((100 )/(y))

Use the quotient property of logs to write as a difference of logarithms. Simplify if possible.\newlinelog⁡(100y)\log\left(\frac{100}{y}\right)\newline

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Full solution

Q. Use the quotient property of logs to write as a difference of logarithms. Simplify if possible.\newlinelog⁡(100y)\log\left(\frac{100}{y}\right)\newline
  1. Identify Property: Identify the property to use for expanding log⁡(100y)\log\left(\frac{100}{y}\right). We need to use the quotient property of logarithms, which states log⁡b(PQ)=log⁡b(P)−log⁡b(Q)\log_b\left(\frac{P}{Q}\right) = \log_b(P) - \log_b(Q).
  2. Apply Quotient Property: Apply the quotient property to log⁡(100y)\log\left(\frac{100}{y}\right). Using the property, log⁡(100y)=log⁡(100)−log⁡(y)\log\left(\frac{100}{y}\right) = \log(100) - \log(y).

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