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GATE 2024 EC – Question 4

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

For a real number $x>1$,

$$\frac{1}{\log_2x}+\frac{1}{\log_3x}+\frac{1}{\log_4x}=1$$

The value of $x$ is

  1. 4
  2. 12
  3. 24
  4. 36

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Correct answer: (C) 24

Explanation

$\dfrac1{\log_ax}=\log_xa$, so the sum is $\log_x2+\log_x3+\log_x4=\log_x24=1$, which gives $x=24$.