Log₂(9 - 2ˣ) = 3 - x
2⁽³ ⁻ ˣ) = 9 - 2ˣ
2³ / 2ˣ = 9 - 2ˣ
8 = 9 ·2ˣ - 2²ˣ
2²ˣ - 9 ·2ˣ + 8 = 0
Замена t = 2ˣ
t² - 9t + 8 = 0
D = 81 - 32 = 49 √D = 7
t1 = 0.5 (9 - 7) = 1 тогда 1 = 2ˣ → х1= 0
t1 = 0.5 (9 + 7) = 8 тогда 8 = 2ˣ → х2= 3
Ответ: х1 = 0; х2 = 3