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Olabushka98
@Olabushka98
July 2022
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lg^2x+4lg(10x)=1 решите пожалуйста
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Lg^2x+4lg(10x)=1Lg^2(x) + 4*(Lg10 + Lgx) = 1
Lg^2(x) + 4*(1 + Lgx) = 1
Lg^2(x) + 4 + 4*Lgx = 1
Lg^2(x) + 4*Lgx + 3 = 0
Замена: Lg(x) = y, тогда
y^2 + 4y + 3 = 0, D = 16 - 12 = 4,
y1 = (-4 + 2)/2 = - 1,
y2 = (-4 - 2)/2 = - 3, Обратная замена: Lg(x) = y1 = -1, x = 10^(-1) =1/10 = 0.1
Lg(x) = y2 = -3, x = 10^(-3) =1/1000 = 0,001
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Verified answer
Lg^2x+4lg(10x)=1Lg^2(x) + 4*(Lg10 + Lgx) = 1Lg^2(x) + 4*(1 + Lgx) = 1
Lg^2(x) + 4 + 4*Lgx = 1
Lg^2(x) + 4*Lgx + 3 = 0
Замена: Lg(x) = y, тогда
y^2 + 4y + 3 = 0, D = 16 - 12 = 4,
y1 = (-4 + 2)/2 = - 1,
y2 = (-4 - 2)/2 = - 3, Обратная замена: Lg(x) = y1 = -1, x = 10^(-1) =1/10 = 0.1
Lg(x) = y2 = -3, x = 10^(-3) =1/1000 = 0,001