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Rewrite the following in the form log(c). log(3)+log(5)

Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(3)+log⁡(5) \log (3)+\log (5)

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Q. Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(3)+log⁡(5) \log (3)+\log (5)
  1. Identify property for combining logarithms: log⁡(3)+log⁡(5)\log(3) + \log(5)\newlineIdentify the property that can be used to combine the two logarithms.\newlineSum of logarithms of two numbers equals the logarithm of their product.\newlineProduct property: log⁡(P)+log⁡(Q)=log⁡(P×Q)\log(P) + \log(Q) = \log(P \times Q)
  2. Apply product property of logarithms: log⁡(3)+log⁡(5)\log(3) + \log(5)\newlineApply the product property of logarithms to combine the two logs into one.\newlinelog⁡(3)+log⁡(5)=log⁡(3×5)\log(3) + \log(5) = \log(3 \times 5)
  3. Calculate product of 33 and 55: Calculate the product of 33 and 55.\newline3×5=153 \times 5 = 15\newlineSo, log⁡(3×5)=log⁡(15)\log(3 \times 5) = \log(15)
  4. Rewrite expression as single logarithm: Rewrite the expression as a single logarithm. \newlinelog⁡(3)+log⁡(5)=log⁡(15)\log(3) + \log(5) = \log(15)\newlineThis is the expression in the form log⁡(c)\log(c).

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