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

Rewrite the following in the form log⁡(c) \log (c) .\newline2log⁡(3) 2 \log (3)

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Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newline2log⁡(3) 2 \log (3)
  1. Given expression: We are given the expression 2log⁡(3)2\log(3) and we need to rewrite it in the form log⁡(c)\log(c). We can use the power property of logarithms to do this. The power property states that n⋅log⁡b(a)=log⁡b(an)n \cdot \log_b(a) = \log_b(a^n).
  2. Apply power property: Apply the power property to 2log⁡(3)2\log(3). \newline2log⁡(3)=log⁡(32)2\log(3) = \log(3^2)
  3. Calculate value: Calculate the value of 323^2.\newline32=3×3=93^2 = 3 \times 3 = 9
  4. Replace with calculated value: Replace 323^2 with its calculated value in the logarithmic expression.\newlinelog⁡(32)=log⁡(9)\log(3^2) = \log(9)
  5. Rewritten expression: We have now rewritten the expression 2log⁡(3)2\log(3) in the form log⁡(c)\log(c), where cc is 99.

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