ln(x)-3/ln(x)=2

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

D( x )

x <= 0

ln(x) = 0

x <= 0

ln(x) = 0

ln(x) = 0

ln(x) = ln(e^0)

x = e^0

x = 1

x in (0:1) U (1:+oo)

ln(x)-(3/ln(x)) = 2 // - 2

ln(x)-(3/ln(x))-2 = 0

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

k_1 = ln(x)

1*k_1^1-3*k_1^-1-2*k_1^0 = 0

(1*k_1^2-2*k_1^1-3*k_1^0)/(k_1^1) = 0 // * k_1^2

k_1^1*(1*k_1^2-2*k_1^1-3*k_1^0) = 0

k_1^1

k_1^2-2*k_1-3 = 0

k_1^2-2*k_1-3 = 0

DELTA = (-2)^2-(-3*1*4)

DELTA = 16

DELTA > 0

k_1 = (16^(1/2)+2)/(1*2) or k_1 = (2-16^(1/2))/(1*2)

k_1 = 3 or k_1 = -1

k_1 in { -1, 3} 

ln(x) = -1

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

x = e^-1

ln(x) = 3

ln(x) = ln(e^3)

x = e^3

x in { e^-1, e^3 }