ln(x-3)=ln(1/x)

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Solution for ln(x-3)=ln(1/x) equation: 


D( x )

x = 0

1/x <= 0

x-3 <= 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-3 <= 0

x-3 <= 0

x-3 <= 0 // + 3

x <= 3

x in (3:+oo)

ln(x-3) = ln(1/x) // - ln(1/x)

ln(x-3)-ln(1/x) = 0

ln(1*(x-3))-ln(1/x) = 0

ln((1*(x-3))/(1/x)) = 0

ln((x-3)/(1/x)) = 0

ln((x-3)/(1/x)) = ln(e^0)

(x-3)/(1/x) = e^0

(x-3)/(1/x)-e^0 = 0

(x-3)/(x^-1)-1 = 0

(x-3)/(x^-1)+(-1*x^-1)/(x^-1) = 0

x-1*x^-1-3 = 0

x-x^-1-3 = 0

x-x^-1-3 = 0

1*x^1-1*x^-1-3*x^0 = 0

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

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

x^1

x^2-3*x-1 = 0

x^2-3*x-1 = 0

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

DELTA = 13

DELTA > 0

x = (13^(1/2)+3)/(1*2) or x = (3-13^(1/2))/(1*2)

x = (13^(1/2)+3)/2 or x = (3-13^(1/2))/2

x in { (3-13^(1/2))/2, (13^(1/2)+3)/2} 

(x-((3-13^(1/2))/2))*(x-((13^(1/2)+3)/2)) = 0

((x-((3-13^(1/2))/2))*(x-((13^(1/2)+3)/2)))/(x^-1) = 0

((x-((3-13^(1/2))/2))*(x-((13^(1/2)+3)/2)))/(x^-1) = 0 // * 1/x

(x-((3-13^(1/2))/2))*(x-((13^(1/2)+3)/2)) = 0

( x-((13^(1/2)+3)/2) )

x-((13^(1/2)+3)/2) = 0 // + (13^(1/2)+3)/2

x = (13^(1/2)+3)/2

( x-((3-13^(1/2))/2) )

x-((3-13^(1/2))/2) = 0 // + (3-13^(1/2))/2

x = (3-13^(1/2))/2

x in { (3-13^(1/2))/2} 

x = (13^(1/2)+3)/2

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