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NDA 1 2024 Maths, question 7

Topic: Algebra

Q7

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

  1. (a) bd2f3bd^{2}f^{3}Correct answer
  2. (b) bdfbdf
  3. (c) b3d2fb^{3}d^{2}f
  4. (d) b2d2f2b^{2}d^{2}f^{2}

Solution.

Answer: (a) bd2f3bd^{2}f^{3}

  1. Rewrite the logarithms as a=bᵖ, c=d²ᵖ and e=f³ᵖ.
  2. Then ace=(bd²f³)ᵖ, so (ace)^(1/p)=bd²f³.
  3. The displayed expression requires p≠0, with positive admissible logarithm bases.