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GATE 2026 EC – Question 4

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

Real numbers $y$, $p$, and $n$ (all greater than 1) satisfy $(\log_{p^{1/n}} y)(\log_{y^{1/n}} p) = 16$, where the logarithms are taken to the bases $p^{1/n}$ and $y^{1/n}$. The value of $n$ is ________.

  1. 2
  2. 4
  3. 8
  4. 16

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Correct answer: (B) 4

Explanation

$\log_{p^{1/n}} y = n\log_p y$ and $\log_{y^{1/n}} p = n\log_y p$. Their product is $n^2(\log_p y)(\log_y p) = n^2 = 16$, so $n=4$.