Question

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Answer 1

Given: $x=\log_{0.1}0.001,y=\log_{9}81$

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Solution

[Value of $x$ ]

$\implies x=\log_{10^{-1}}10^{-3}$

$\implies x=\dfrac{-3}{-1} \log_{10}10$

$\implies \boxed{x=3}$

[Value of $y$ ]

$\implies y=\log_{9}9^2$

$\implies \boxed{y=2}$

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Now we calculate the square root,

$\implies \sqrt{x-2\sqrt{y} } =\sqrt{3-2\sqrt{2} } =\sqrt{2} -1$