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Question: Answered & Verified by Expert
If $\quad x=\log _{0.1} 0.001, \quad y=\log _9 81, \quad$ then $\sqrt{x-2 \sqrt{y}}$ is equal to
MathematicsFunctionsTS EAMCETTS EAMCET 2001
Options:
  • A $3-\sqrt{2}$
  • B $\sqrt{3}-2$
  • C $\sqrt{2}-1$
  • D $\sqrt{2}-2$
Solution:
1772 Upvotes Verified Answer
The correct answer is: $\sqrt{2}-1$
Since, $x=\log _{0.1}(0.1)^3=3 \log _{0.1} 0.1=3$
Now, $\begin{aligned} y & =\log _9 81=\log _9 9^2=2 \\ & =\sqrt{(\sqrt{2}-1)^2}=\sqrt{2}-1\end{aligned}$

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