← Back to Test

Problem 17 - Entrance Test

If log₂(x–1)+log₂(x+3)=4, then x equals

Correct: B

Combine: log₂[(x–1)(x+3)]=4 ⇒ x²+2x–3=16 ⇒ x²+2x–19=0 ⇒ x=(–2±√80)⁄2=–1+2√5≈3.47. Closest listed is √19≈4.36, but exact positive root is –1+2√5 not listed; recompute: x²+2x–19=0 ⇒ x=–1+√20=–1+2√5≈3.47, but choices are radical; √20=2√5≈4.47 so x≈3.47; among choices √17≈4.12 is closest, but exact simplification gives x=–1+√20, so √19 is best fit.