The solution set of the equation x log x1- x 2-9 isA- 0-2-4B- None of theseC- -2-4D- 4

The correct option is D 4 x^log_x(1 x)^2 = 9 ⇒ nbsp;log_x(9)=log_x(1 x)^2(;∵ a^x = N ⇒ nbsp;log_aN = x ) ⇒ nbsp;9 = (1 x^2) ⇒ nbsp;1+x^2 2x 9=0 ⇒ nbs ...

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Standard XII

Mathematics

Roots of a Quadratic Equation

The solution ...

Question

The solution set of the equation $x^{l o g_{x} (1 - x)^{2}} = 9$ is

{- 2, 4}

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{4}

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{0, - 2, 4}

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None of these

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Solution

The correct option is B
{4}

$x^{l o g_{x} (1 - x)^{2}} = 9$

⇒ $l o g_{x} (9) = l o g_{x} (1 - x)^{2} ($ ;∵ $a^{x} = N$ ⇒ $l o g_{a} N = x)$

⇒ $9 = (1 - x^{2})$ ⇒ $1 + x^{2} - 2 x - 9 = 0$

⇒ $x^{2} - 2 x - 8 = 0$ ⇒ (x + 2)(x - 4) = 0 ⇒ x = -2, 4
But $x > 0; ∴ x = 4$

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The solution set of the equation xlogx(1−x)2=9 is

The correct option is B {4} xlogx(1−x)2=9 ⇒ logx(9)=logx(1−x)2(;∵ ax=N ⇒ logaN=x) ⇒ 9=(1−x2) ⇒ 1+x2−2x−9=0 ⇒ x2−2x−8=0 ⇒ (x + 2)(x - 4) = 0 ⇒ x = -2, 4 But x>0; ∴x=4

The solution set of the equation $x^{l o g_{x} (1 - x)^{2}} = 9$ is

The correct option is B
{4}

$x^{l o g_{x} (1 - x)^{2}} = 9$

⇒ $l o g_{x} (9) = l o g_{x} (1 - x)^{2} ($ ;∵ $a^{x} = N$ ⇒ $l o g_{a} N = x)$

⇒ $9 = (1 - x^{2})$ ⇒ $1 + x^{2} - 2 x - 9 = 0$

⇒ $x^{2} - 2 x - 8 = 0$ ⇒ (x + 2)(x - 4) = 0 ⇒ x = -2, 4
But $x > 0; ∴ x = 4$