If \log_{b}a=p, \log_{d}c=2p and \log_{f}e=3p, then what is (ace)^{\frac{1}{p}} equal to?

  1. A. bd^{2}f^{3}
  2. B. bdf
  3. C. b^{3}d^{2}f
  4. D. b^{2}d^{2}f^{2}

Correct Answer: A. bd^{2}f^{3}

Explanation

From the definition of logarithms, a = b^p, c = d^{2p}, and e = f^{3p}. Multiplying them gives ace = b^p d^{2p} f^{3p} = (bd^2f^3)^p. Raising both sides to the power of \frac{1}{p} gives (ace)^{\frac{1}{p}} = bd^2f^3.

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