Ln(x)-ln(1/x)=2

Solution for Ln(x)-ln(1/x)=2 equation:

D( x )

x <= 0

x = 0

1/x <= 0

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

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

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

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

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

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

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

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

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

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

x^2 = e^2

x^2 = e^2 // ^ 1/2

abs(x) = e

x = e or x = -e

x in { -e} 

x = e