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 DA 2026 Q4: Compare n^(log m) and m^(log n)

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 _______.

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: C (official GATE 2026 final answer key)

Concept used: Logarithm identity: $a^{\log b} = b^{\log a}$ .

First step: Take $\log_{10}$ of both: $\log x = \log m \cdot \log n = \log y$ .

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key