If ${log}_{2} (8 X - X^{2} - 7) = {log}_{2} (X^{4} - 12 X^{3} + 40 X^{2} - 34 X - 7),$ then possible value of X is/are

X = 2

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X = 0

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X = 3

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X = 7

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Solution

The correct option is D $X = 0$
$8 X - X^{2} - 7 = X^{4} - {12 X}^{3} + {40 X}^{2} - 34 X - 7$
${12 X}^{3} - {42 X}^{2} + 42 X = 0$
$X ({12 X}^{2} - 42 X + 42) = 0$
$7 X ({2 X}^{2} + 7 X + 7) = 0$
$X = 0$
Hence no value of X is possible.

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