Consider two distinct positive real numbers m, n, with m > n. Let x = n 10(m) and y = m 10(n). The relation between x and y is .

GATE 2026 DA – Question 4

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

Consider two distinct positive real numbers $m$, $n$, with $m > n$.

Let $x = n^{\log_{10}(m)}$ and $y = m^{\log_{10}(n)}$. The relation between $x$ and $y$ is _______.

$x > y$
$x < y$
$x = y$
$x = \log_{10}(y)$

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Correct answer: (C) $x = y$

Explanation

Take $\log_{10}$ of both: $\log_{10}x = \log_{10}(m)\cdot\log_{10}(n)$ and $\log_{10}y = \log_{10}(n)\cdot\log_{10}(m)$. The two are the same, so $x = y$.