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Legox
@Legox
July 2022
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Помогите решить или объясните решение, пожалуйста:
3^3x-11*3^2x+18*3^x=0
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nKrynka
Решение
3^3(x) -11*3^2(x) + 18*3^(x) = 0
3^x * (3^(2x) - 11*(3^x) + 18) = 0
3^x = 0 не имеет смысла
(3^(2x) - 11*(3^x) + 18) = 0
3^x = Z
z^2 - 11z + 18 = 0
D = 11^2 - 4*1*18 = 121 - 72 = 49
Z1 = (11 - 7)/2 = 2
Z2 = (11+ 7)/2 = 9
3^x = 2
log(3^x) = log2
x*log3 (3) = log2
x1 = log2
3^x = 9
3^x = 3^2
x2 = 2
Ответ: x1 = log2: х2 = 2.
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Answers & Comments
3^3(x) -11*3^2(x) + 18*3^(x) = 0
3^x * (3^(2x) - 11*(3^x) + 18) = 0
3^x = 0 не имеет смысла
(3^(2x) - 11*(3^x) + 18) = 0
3^x = Z
z^2 - 11z + 18 = 0
D = 11^2 - 4*1*18 = 121 - 72 = 49
Z1 = (11 - 7)/2 = 2
Z2 = (11+ 7)/2 = 9
3^x = 2
log(3^x) = log2
x*log3 (3) = log2
x1 = log2
3^x = 9
3^x = 3^2
x2 = 2
Ответ: x1 = log2: х2 = 2.