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GATE 2018 ME (ME2) – Question 5

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

Evaluate $\frac1{1+\log_u(vw)}+\frac1{1+\log_v(wu)}+\frac1{1+\log_w(uv)}$.

  1. −1
  2. 0
  3. 1
  4. 3

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Correct answer: (C) 1

Explanation

Set $a=\ln u$, $b=\ln v$, $c=\ln w$. Then $1+\log_u(vw)=(a+b+c)/a$, so the first term is $a/(a+b+c)$. The other terms are $b/(a+b+c)$ and $c/(a+b+c)$. Their sum is **1, C**, where the original logarithms and denominators exist.