ln(1/x)=-5

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Solution for ln(1/x)=-5 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) = -5 // + 5

ln(1/x)+5 = 0

ln(1/x)+5 = 0 // - 5

ln(1/x) = -5

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

1/x = e^-5

1/x-e^-5 = 0

1*x^-1 = e^-5 // : 1

x^-1 = e^-5

-1 < 0

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

1 = e^-5*x^1 // : e^-5

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

x = 1/(e^-5)

x = 1/(e^-5)

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