Q116 / 200 · AP EAMCET 2001 · Mathematics

If $\quad x=\log _{0.1} 0.001, \quad y=\log _9 81, \quad$ then $\sqrt{x-2 \sqrt{y}}$ is equal to

  • A
    $3-\sqrt{2}$
  • B
    $\sqrt{3}-2$
  • Correct answer
    C
    $\sqrt{2}-1$
  • D
    $\sqrt{2}-2$

Solution

Since, $x=\log _{0.1}(0.1)^3=3 \log _{0.1} 0.1=3$ Now, $\begin{aligned} y & =\log _9 81=\log _9 9^2=2 \\ & =\sqrt{(\sqrt{2}-1)^2}=\sqrt{2}-1\end{aligned}$

Hence, the correct answer is option: 'C'.

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