De logaritmische vergelijking
(log2 x)2 − 4.log2 x + 3 = 0
bezit twee oplossingen.
De som van die twee oplossingen is 		A.   10
B.   8
C.   6
D.   4
E.   12
A    B    C    D    E

[ 6-2476 - op net sinds 17.11.13-(E)-25.10.2023 ]

Translation in   E N G L I S H

The equation
(log2 x)2 − 4(log2 x) + 3 = 0
has two solutions.
What is the sum
of those two solutions ? 		A.   10
B.   8
C.   6
D.   4
E.   12

Oplossing - Solution

  (log2 x)2 − 4.log2 x + 3 = 0
⇔ y² − 4y + 3 = 0   ∧  y = log2 x
⇔ (y − 1)(y − 3) = 0  ∧  y = log2 x
⇔ [ y = 1 ∨ y = 3 ]   ∧  y = log2 x
⇔ log2 x = 1 ∨ log2 x =3
⇔ x = 2 ∨ x = 8