Let S be the set of all real roots of the equation, 3x3x−1+2=3x−1+3x−2. Then S:

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Let S be the set of all real roots of the equation, $3^{x} (3^{x} - 1) + 2 = |3^{x} - 1| + |3^{x} - 2|$ . Then S:

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is an empty set

is a singleton

contains at least four elements

contains exactly two elements

answer is B.

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Detailed Solution

Let $3^{x} = t$ , then t > 0 and

$\begin{array}{l} t (t - 1) + 2 = | t - 1 | + | t - 2 | \\ t^{2} - t + 2 = | t - 1 | + | t - 2 | \end{array}$

On + ve side of x – axis, there is only one point of intersection

$∴ t = a \Rightarrow x = \log_{3} a$

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