ln(1/x)=-1

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Solution for ln(1/x)=-1 equation: 


D( x )

x = 0

1/x <= 0

x = 0

x = 0

1/x <= 0

1/x <= 0

1*x^-1 <= 0

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

x^-1 <= 0/1

x^-1 <= 0

1/(x^1) <= 0

x <> 0

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

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

x^1 <= 0

x <= 0

x in (-oo:0)

x in (0:+oo)

ln(1/x) = -1 // + 1

ln(1/x)+1 = 0

ln(1/x)+1 = 0 // - 1

ln(1/x) = -1

ln(1/x) = ln(e^-1)

1/x = e^-1

1/x-e^-1 = 0

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

x^-1 = e^-1

-1 < 0

1/(x^1) = e^-1 // * x^1

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

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

x = 1/(e^-1)

x = 1/(e^-1)

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