ln((1/x^2))=10

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Solution for ln((1/x^2))=10 equation: 


D( x )

1/(x^2) <= 0

x^2 = 0

1/(x^2) <= 0

1/(x^2) <= 0

1*x^-2 <= 0

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

x^-2 <= 0/1

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^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

ln(1/(x^2)) = 10 // - 10

ln(1/(x^2))-10 = 0

ln(1/(x^2))-10 = 0 // + 10

ln(1/(x^2)) = 10

ln(1/(x^2)) = ln(e^10)

1/(x^2) = e^10

1/(x^2)-e^10 = 0

1*x^-2 = e^10 // : 1

x^-2 = e^10

-2 < 0

1/(x^2) = e^10 // * x^2

1 = e^10*x^2 // : e^10

1/(e^10) = x^2

x^2 = 1/(e^10) // ^ 1/2

abs(x) = 1/(e^5)

x = 1/(e^5) or x = -(1/(e^5))

x in { 1/(e^5), -(1/(e^5)) }

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