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marknefedov
@marknefedov
June 2022
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Решите уравнение: 4^x - 5*2^x +6=0
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nKrynka
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
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Answers & Comments
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