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Rewrite the following in the form log(c). log(4)+log(5)

Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(4)+log⁡(5) \log (4)+\log (5)

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Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(4)+log⁡(5) \log (4)+\log (5)
  1. Identify Property: Identify the property of logarithm used to combine log⁡(4)\log(4) and log⁡(5)\log(5). When adding two logarithms with the same base, we can use the product property to combine them into a single logarithm.
  2. Apply Property: Apply the product property to combine log⁡(4)\log(4) and log⁡(5)\log(5). According to the product property, log⁡(a)+log⁡(b)=log⁡(ab)\log(a) + \log(b) = \log(ab). Therefore, log⁡(4)+log⁡(5)=log⁡(4×5)\log(4) + \log(5) = \log(4 \times 5).
  3. Perform Multiplication: Perform the multiplication inside the logarithm.\newlineCalculate 4×54 \times 5 to get 2020.\newlineSo, log⁡(4)+log⁡(5)=log⁡(20)\log(4) + \log(5) = \log(20).

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