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Rewrite the following in the form log(c). log(4)+log(3)

Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(4)+log⁡(3) \log (4)+\log (3)

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Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(4)+log⁡(3) \log (4)+\log (3)
  1. Identify logarithm property: log⁡(4)+log⁡(3)\log(4) + \log(3)\newlineIdentify the property of logarithms that can be used to combine the two terms.\newlineSum of logarithms property: log⁡bP+log⁡bQ=log⁡b(PQ)\log_b P + \log_b Q = \log_b (PQ)
  2. Combine logarithms: log⁡(4)+log⁡(3)\log(4) + \log(3)\newlineApply the sum of logarithms property to combine the two logarithms into one.\newlinelog⁡(4)+log⁡(3)=log⁡(4×3)\log(4) + \log(3) = \log(4 \times 3)
  3. Calculate product: Calculate the product of 44 and 33.\newline4×3=124 \times 3 = 12\newlineSo, log⁡(4×3)=log⁡(12)\log(4 \times 3) = \log(12)
  4. Rewrite as single logarithm: Rewrite the expression as a single logarithm. \newlinelog⁡(4)+log⁡(3)=log⁡(12)\log(4) + \log(3) = \log(12)\newlineThis is the expression in the form log⁡(c)\log(c).

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