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Rewrite the following in the form log(c). log(15)-log(3)

Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(15)−log⁡(3) \log (15)-\log (3)

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Q. Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(15)−log⁡(3) \log (15)-\log (3)
  1. Property Simplification: log⁡(15)−log⁡(3)\log(15) - \log(3)\newlineWhich property can be used to simplify the expression?\newlineDifference of logarithms of two numbers equals the logarithm of their division.\newlineQuotient property: log⁡bP−log⁡bQ=log⁡b(PQ)\log_b P - \log_b Q = \log_b \left(\frac{P}{Q}\right)
  2. Apply Quotient Property: log⁡(15)−log⁡(3)\log(15) - \log(3)\newlineApply the quotient property of logarithms.\newlinelog⁡(15)−log⁡(3)=log⁡(153)\log(15) - \log(3) = \log\left(\frac{15}{3}\right)
  3. Calculate Division: Calculate 15/315/3.\newlineDivide 1515 by 33 to get 55.\newline15/3=515/3 = 5
  4. Replace with 55: log⁡(153)\log(\frac{15}{3})\newlineReplace 153\frac{15}{3} with 55.\newlinelog⁡(153)=log⁡(5)\log(\frac{15}{3}) = \log(5)

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