The sum of the real values of $x$ satisfying the equation $2^{(x - 1) (x^{2} + 5 x - 50)} = 1$ is

- 5

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14

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- 4

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16

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Solution

The correct option is B $- 4$
$2^{(x^{2} + 5 x - 50) (x - 1)} = 1$

$2^{(x^{2} + 5 x - 50) (x - 1)} = 2^{0} = 1$

Since the base 2 is same to their powers are equal,

$(x^{2} + 5 x - 50) (x - 1) = 0$

$(x + 10) (x - 5) (x - 1) = 0$

$⟹ x = - 10, 5, 1$

Sum of the values of x=-4

Hence, the option (c) is correct.

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