㏒₂ ² (x-4) - ㏒₂ (x-4) - 12 = 0
notam:
㏒₂ (x-4) = t
acum obtinem:
t² - t - 12 = 0
ecuatie de gradul cu a= 1
b= -1
c= -12
Δ = b² - 4ac
Δ = 49
√Δ = √49
√Δ = 7
-b ± √Δ 1 ± 7
t ₁;₂ = ----------------- = -------------
2 2
t ₁ = (1+7)/2 = 8/2 = 4
t ₂ = (1-7)/2 = - 3
㏒₂ (x-4) = t
㏒₂ (x-4) = 4
2⁴ = x-4
16 = x-4
x₁=20
㏒₂ (x-4) = -3
2⁻³ = x-4
1/2³ = x-4
2³(x-4) = 1
8x - 32 = 1
x₂= 33/8
x₁ ·x₂ = 20 ·33/8 = 165/2
