The number of real roots of the equation $5 + | 2^{x} - 1 | = 2^{x} (2^{x} - 2)$ is:

2

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3

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4

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1

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Solution

The correct option is C $1$
Let $2^{x} = t$ and $t$ is always $+ v e$
$g (t) = 5 + | t - 1 |$
$f (t) = t^{2} - 2 t$

From the graph
$g (t)$ and $f (t)$ intersect at two point
but one value of $t$ is negative
and only one value of $t$ is positive
So, number of real roots is $1$

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