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The solution of set of the equation \( \Large x log x \left(1-x\right)^{2}=9 \) is

A) \( \Large \{ -2, 4 \} \)
B) \( \Large \{ 4 \} \)
C) \( \Large \{ 0, -2, 4 \} \)
D) none of these

Correct Answer:

A) \( \Large \{ -2, 4 \} \)

Description for Correct answer:
We have, \( \Large x^{logx \left(1-x\right)^{2} }=9 \)

Taking log on both sides, we get

\( \Large x \left(9\right)=log x \left(1-x\right)^{2} \left(\because a^{x}=N => log a N = x \right) \)

=> \( \Large 9= \left(1-x\right)^{2} => 1+x^{2}-2x-9=0 \)

=> \( \Large x^{2}-2x-8=0 \)

=> \( \Large x = -2, 4 \)

=> \( \Large x = 4 \left(\because x = 2\right) \)

Part of solved Quadratic Equations questions and answers : >> Elementary Mathematics >> Quadratic Equations

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Similar Questions

1). If x is real the expression \( \Large \frac{x+2}{2x^{2}+3x+6} \) takes all values in the interval:

A). \( \Large \left(\frac{1}{13}, \frac{1}{3}\right) \)

B). \( \Large \left(- \frac{1}{13}, \frac{1}{3}\right) \)

C). \( \Large \left(- \frac{1}{3}, \frac{1}{13}\right) \)

D). none of these.

2). If x is real, then the maximum and minimum values of the expression \( \Large \frac{x^{2}
-3x+4}{x^{2}+3x+4} \) will be:

A). 2,1

B). \( \Large 5, \frac{1}{5} \)

C). \( \Large 7, \frac{1}{7} \)

D). none of these.

3). The number of real solutions of the equation \( \Large |x^{2}+4x+3|+2x+5=0 \) are:

A). 1

B). 2

C). 3

D). 4

4). If the roots of the given equation:
\( \Large \left(\cos p-1\right)x^{2}+ \left(\cos p\right)x+\sin p = 0 \) are real, then:

A). \( \Large P \epsilon \left(- \pi ,0\right) \)

B). \( \Large P \epsilon \left(- \frac{ \pi }{2}, \frac{ \pi }{2} \right) \)

C). \( \Large P \epsilon \left(0, \pi \right) \)

D). \( \Large P \epsilon \left(0, 2 \pi \right) \)

5). The solution of the quadratic equation \( \Large \left(3|x|-3\right)^{2}=|x|+7 \) which belongs to the domain of definition of function \( \Large \gamma = \sqrt{x \left(x-3\right) } \) are given by:

A). \( \Large \pm \frac{1}{9}, \pm 2 \)

B). \( \Large -\frac{1}{9}, 2 \)

C). \( \Large \frac{1}{9}, -2 \)

D). \( \Large -\frac{1}{9}, -2 \)

6). The number of solution of \( \Large \frac{log 5 + log \left(x^{2}+1\right) }{log \left(x-2\right) }=2 \)

A). 2

B). 3

C). 1

D). none of these

7). If the expression \( \Large \left(mx-1+\frac{1}{x}\right) \) is always nonnegative, then the minimum value of m must be:

A). \( \Large -\frac{1}{2} \)

B). 0

C). \( \Large \frac{1}{4} \)

D). \( \Large \frac{1}{2} \)

8). The value of x in the given equation \( \Large 4^{x}-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2x-1} \) is:

A). \( \Large \frac{4}{3} \)

B). \( \Large \frac{3}{2} \)

C). \( \Large \frac{2}{1} \)

D). \( \Large \frac{5}{3} \)

9). The harmonic mean of the roots of equation \( \Large \left(5+\sqrt{2}x^{2}-14+\sqrt{5}\right)x+8+2\sqrt{5}=0 \) is:

A). 2

B). 4

C). 6

D). 8

10). For what value of \( \Large \lambda \) the sum of the squares of the roots of \( \Large x^{2}+ \left(2+\lambda\right)n-\frac{1}{2} \left(1+\lambda\right)=0 \) is minimum?

A). \( \Large \frac{3}{2} \)

B). 1

C). \( \Large \frac{1}{2} \)

D). \( \Large \frac{11}{4} \)