The set of all values of x satisfying $x^{l o g_{x} (1 - x)^{2}} = 9$ is

a subset of R containing N

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a subset of R containing Z(set of all integers)

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is a finite set containing at least two elements

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a finite set

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Solution

The correct option is D
a finite set

Taking algorithm of both the sides with base 3, we have
$l o g_{x} (1 - x)^{2} l o g_{3} x = 2 \Rightarrow \frac{l o g_{3} (1 - x)^{2}}{l o g_{3} x} l o g_{3} x = 2 \Rightarrow l o g_{3} (1 - x)^{2} = 2 \Rightarrow (1 - x)^{2} = 9 (c l e a r l y x \neq 3) \Rightarrow x = 4, - 2. B u t x > 0 \Rightarrow x = 4$

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