ln(1/3x^-2)

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Solution for ln(1/3x^-2) equation:


D( x )

x = 0

(1/3)*x^-2 <= 0

x = 0

x = 0

(1/3)*x^-2 <= 0

(1/3)*x^-2 <= 0

1/3*x^-2 <= 0

1/3*x^-2 <= 0 // : 1/3

x^-2 <= 0/1/3

x^-2 <= 0

1/(x^2) <= 0

x <> 0

1/(x^2) <= 0 // * x^4

(x^4)/(x^2) <= 0

x^2 <= 0

x belongs to the empty set

x in (-oo:0) U (0:+oo)

ln((1/3)*x^-2) = 0

ln((1/3)*x^-2) = ln(e^0)

(1/3)*x^-2 = e^0

(1/3)*x^-2-e^0 = 0

1/3*x^-2 = 1 // : 1/3

x^-2 = 3

-2 < 0

1/(x^2) = 3 // * x^2

1 = 3*x^2 // : 3

1/3 = x^2

x^2 = 1/3 // ^ 1/2

abs(x) = (1/3)^(1/2)

x = (1/3)^(1/2) or x = -(1/3)^(1/2)

x in { (1/3)^(1/2), -(1/3)^(1/2) }

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