First slide

Introduction to real valued functions

Question

$The solution set of the equation x^{\log_{x} (1 - x)^{2}} = 9, is$

Easy

A

${- 2, 4}$
B

${4}$
C

${0, - 2, - 4}$
D

None of these

Solution

$\begin{array}{l} x^{\log_{x} (1 - x)^{2}} = 9 \\ \Rightarrow (1 - x)^{2} = 9 \\ \Rightarrow 1 - x = \pm 3 \\ \Rightarrow x = - 2, 4 \\ But x = - 2 is not possible \\ \Rightarrow x = 4 \end{array}$

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