The solution set of the equation $l o g_{2} (3 - x) + l o g_{2} (1 - x) = 3$ is?

{- 1, 5}

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{- 1}

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{5}

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ϕ

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Solution

The correct option is D ${- 1}$
The equation will be meaningful if $x < 1$ . The equation reduces to
${log}_{2} (3 - x) (1 - x) = 3$

from which we obtain $(3 - 1) (1 - x) = 2^{3} = 8$ or $x^{2} - 4 x - 5 = 0$ . Its roots are $- 1$ and $5$ .

The root $5$ is rejected since it does not satisfy the condition $x < 1$ .

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