Question

If log₂ x + log₂ (x – 1) = 1, then find the value of x.

Answer 1

log₂x + log₂(x – 1) = 1

⇒ log₂ x(x – 1) = 1

⇒ x(x – 1) = 2¹

⇒ x² – x – 2 = 0

⇒ x² – 2x + x – 2 = 0

⇒ (x – 2) (x + 1) = 0

⇒ x = 2, x = – 1

Negative value for algorithm is not possible

∴ x = 2