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

Rewrite the following in the form log⁡(c) \log (c) .\newline4log⁡(3) 4 \log (3)

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Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newline4log⁡(3) 4 \log (3)
  1. Identify expression to rewrite: Identify the expression to be rewritten.\newlineWe have the expression 4log⁡(3)4\log(3) and we need to rewrite it in the form log⁡(c)\log(c).
  2. Apply power property of logarithms: 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 4log⁡(3)4\log(3) as log⁡(34)\log(3^4).
  3. Calculate value of c: Calculate 33^44 to find the value of c.\newline33^44 = 33 \times 33 \times 33 \times 33 = 8181\newlineSo, 44\log(33) can be rewritten as \log(8181).
  4. Check final expression: Check the final expression to ensure it is in the form log⁡(c)\log(c).\newlineThe final expression is log⁡(81)\log(81), which is in the form log⁡(c)\log(c) where c=81c = 81.

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