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Rewrite the following in the form log(c). log(3)+log(2)

Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(3)+log⁡(2) \log (3)+\log (2)

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Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(3)+log⁡(2) \log (3)+\log (2)
  1. Combine logarithms using product property: We will use the product property of logarithms to combine log⁡(3)\log(3) and log⁡(2)\log(2) into a single logarithm. The product property states that the sum of two logarithms with the same base is equal to the logarithm of the product of their arguments.\newlineCalculation: log⁡(3)+log⁡(2)=log⁡(3×2)\log(3) + \log(2) = \log(3 \times 2)
  2. Multiply arguments to find value of c: Now we multiply the arguments of the logarithms to find the value of cc.\newlineCalculation: 3×2=63 \times 2 = 6\newlineSo, log⁡(3)+log⁡(2)\log(3) + \log(2) is equivalent to log⁡(6)\log(6).

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