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GATE 2026 MT – Question 2

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

If a positive real number $x$ satisfies $\log_2x+\log_{\sqrt2}x=48$, then the value of $x$ is ________.

  1. $2^{16}$
  2. $4^{16}$
  3. $2^{14}$
  4. $4^{14}$

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Correct answer: (A) $2^{16}$

Explanation

Change the second logarithm to base 2: $\log_{\sqrt2}x=\log_2x/\log_2\sqrt2=2\log_2x$. Hence $3\log_2x=48$, giving $\log_2x=16$.

Therefore $x=2^{16}$, **A**. This value is positive, as required.