Question

Решите уравнение: 4^x - 5*2^x +6=0

Answer 1

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