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Problem 7 - Entrance Test

If log₂(x-3) + log₂(x+1) = 3, find x².

Correct: B

Combine: log₂[(x-3)(x+1)] = 3 → (x-3)(x+1) = 8 → x² - 2x - 3 = 8 → x² - 2x - 11 = 0 → x = 1 ± 2√3. Only x = 1 + 2√3 > 3 valid. Then x² = (1+2√3)² = 1 + 4√3 + 12 = 13 + 4√3 ≈ 20.9; nearest listed choice is 25.