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GATE 2015 EC – Question 5

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

If $\log_x(5/7) = -1/3$, then the value of $x$ is

  1. 343/125
  2. 125/343
  3. -25/49
  4. -49/25

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Correct answer: (A) 343/125

Explanation

Rewrite the logarithm as $x^{-1/3} = \frac{5}{7}$. Raising both sides to the power $-3$ gives $x = \left(\frac{7}{5}\right)^3 = \frac{343}{125}$.