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Snovad
@Snovad
November 2021
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Номер 2 под буквой а.Номер 3 под буквой б.
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Dимасuk
Verified answer
2. а) 4²ˣ - 2²ˣ⁺⁴ + 15 = 0
2⁴ˣ - 16·2²ˣ + 15 = 0
Пусть t = 2²ˣ, t > 0.
t² - 16t + 15 = 0
t² - 15t - t + 15 = 0
t(t - 15) - (t - 15) = 0
(t - 1)(t - 15) = 0
t = 1; 15
Обратная замена:
2²ˣ = 1
2x = 0
x = 0
или
2²ˣ = 15
2x = log₂15
x = 0,5log₂15
x = log₄15
Ответ: x = 0; log₄15
.
3. б) lg5·lg20 + lg²2 = lg(10/2)·lg(10·2) + lg²2 = (lg10 - lg2)(lg10 + lg2) + lg²2 = lg²10 - lg²2 + lg²2 = lg²10 = 1
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Answers & Comments
Verified answer
2. а) 4²ˣ - 2²ˣ⁺⁴ + 15 = 02⁴ˣ - 16·2²ˣ + 15 = 0
Пусть t = 2²ˣ, t > 0.
t² - 16t + 15 = 0
t² - 15t - t + 15 = 0
t(t - 15) - (t - 15) = 0
(t - 1)(t - 15) = 0
t = 1; 15
Обратная замена:
2²ˣ = 1
2x = 0
x = 0
или
2²ˣ = 15
2x = log₂15
x = 0,5log₂15
x = log₄15
Ответ: x = 0; log₄15.
3. б) lg5·lg20 + lg²2 = lg(10/2)·lg(10·2) + lg²2 = (lg10 - lg2)(lg10 + lg2) + lg²2 = lg²10 - lg²2 + lg²2 = lg²10 = 1