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The number of real roots of the equation...

The number of real roots of the equation
`5+|2^(x)-1|=2^(x)(2^(x)-2)` is

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The correct Answer is:
1
`5 + |2^(x)-1| = 2^(x) (2^(x) -2)` solution will exist only for `x gt0` as for `x lt 0` R.H.S. is negative.
For `x gt 0`
Let `2^(x) = t`
`t^(2) -3t -4 = 0`
`(t-4) (t + 1) = 0`
`t = 4, t ne -1`
`2^(x) = 4 rArr x = 2` only one solution.
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