Решите уравнение: 4^x - 5*2^x + 6=0

Решение

4^x - 5*2^x + 6 = 0

2^ (2x) - 5*2^x + 6 = 0

2 ^x = t, y > 0

t² - 5t + 6 = 0

t₁ = 2

t₂ = 3

1) 2^x = 2

x₁ = 1

2) 2^x = 3

log₂ (2^x) = log₂ 3

x log₂ 2 = log₂ 3

x₂ = log₂ 3

Ответ: x₁ = 1; x₂ = log₂ 3