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

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

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Q. Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(2)+log⁡(2) \log (2)+\log (2)
  1. Understanding logarithm properties: Understand the properties of logarithms.\newlineWe are given log⁡(2)+log⁡(2)\log(2) + \log(2) and need to simplify it using the properties of logarithms. One of the properties of logarithms is that the sum of two logarithms with the same base can be combined into a single logarithm by multiplying the arguments. This is known as the product rule for logarithms.
  2. Applying the product rule: Apply the product rule for logarithms.\newlineUsing the product rule, we can combine log⁡(2)+log⁡(2)\log(2) + \log(2) into a single logarithm by multiplying the arguments (2(2 and 2)2).\newlineSo, log⁡(2)+log⁡(2)=log⁡(2×2)\log(2) + \log(2) = \log(2 \times 2).
  3. Performing multiplication inside the logarithm: Perform the multiplication inside the logarithm.\newlineMultiply the arguments to get the new argument for the combined logarithm.\newline2×2=42 \times 2 = 4\newlineSo, log⁡(2)+log⁡(2)=log⁡(4)\log(2) + \log(2) = \log(4).
  4. Writing the final answer: Write the final answer.\newlineThe simplified form of log⁡(2)+log⁡(2)\log(2) + \log(2) is log⁡(4)\log(4).

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