Question

Calculati:
4^x-7*2^x+12=0

Answer 1

Răspuns:

Explicație pas cu pas:

4ˣ - 7·2ˣ + 12 = 0 <=> (2²)ˣ -7·2ˣ +12 = 0 <=> 2²ˣ - 7·2ˣ +12 = 0

2ˣ = t  => t²-7t+12 = 0 => t₁,₂ = [7±√(49-48)]/2 = (7±1)/2

t₁ = 6/2 = 3  ; t₂ = 8/2 = 4

t₁ = 3 => 2ˣ = 3 => x = log₂3

t₂ = 4 => 2ˣ = 2² => x = 2