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

Rewrite the following in the form log⁡(c) \log (c) .\newline2log⁡(2) 2 \log (2)

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Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newline2log⁡(2) 2 \log (2)
  1. Identify Expression: Identify the expression to be rewritten.\newlineWe have the expression 2log⁡(2)2\log(2), which we want to rewrite in the form log⁡(c)\log(c).
  2. Apply Power Property: Apply the power property of logarithms to rewrite the expression.\newlineThe power property of logarithms states that n⋅log⁡b(a)=log⁡b(an)n \cdot \log_b(a) = \log_b(a^n). We can use this property to rewrite 2log⁡(2)2\log(2) as log⁡(22)\log(2^2).
  3. Calculate Value: Calculate the value of 222^2. 222^2 equals 44. So, log⁡(22)\log(2^2) becomes log⁡(4)\log(4).
  4. Write Final Expression: Write the final expression.\newlineThe expression 2log⁡(2)2\log(2) has been rewritten as log⁡(4)\log(4), which is in the form log⁡(c)\log(c) where c=4c = 4.

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