ln(2x-3)=ln(3/x-1)

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Solution for ln(2x-3)=ln(3/x-1) equation: 


D( x )

x = 0

3/x-1 <= 0

2*x-3 <= 0

x = 0

x = 0

3/x-1 <= 0

3/x-1 <= 0

3*x^-1 <= 1

3*x^-1 <= 1 // : 3

x^-1 <= 1/3

1/(x^1) <= 1/3

x <> 0

1/(x^1) <= 1/3 // * x^2

(x^2)/(x^1) <= 1/3*x^2

x^1 <= 1/3*x^2

x-1/3*x^2 <= 0

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

x < 0

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

1/3*(abs(x))^1+1 >= 0

1/3*(abs(x))^1 >= -1 // : 1/3

(abs(x))^1 >= -1/1/3

(abs(x))^1 >= -3 // ^ 1/1

abs(x) >= (-3)^(1/1)

abs(x) >= -3

x in (-oo:0)

x < 0

x > 0

x^1*(1-(1/3*x^1)) <= 0 // : x^1

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

1 <= 1/3*x^1 // : 1/3

1/1/3 <= x^1 // ^ 1/1

(1/1/3)^(1/1) <= x

x in <3:+oo)

x > 0

x in (-oo:0) U <3:+oo)

2*x-3 <= 0

2*x-3 <= 0

2*x-3 <= 0 // + 3

2*x <= 3 // : 2

x <= 3/2

x in (3/2:3)

ln(2*x-3) = ln(3/x-1) // - ln(3/x-1)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

x^1

2*x^2-2*x-3 = 0

2*x^2-2*x-3 = 0

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

DELTA = 28

DELTA > 0

x = (28^(1/2)+2)/(2*2) or x = (2-28^(1/2))/(2*2)

x = (2*7^(1/2)+2)/4 or x = (2-2*7^(1/2))/4

x in { (2-2*7^(1/2))/4, (2*7^(1/2)+2)/4} 

(x-((2-2*7^(1/2))/4))*(x-((2*7^(1/2)+2)/4)) = 0

((x-((2-2*7^(1/2))/4))*(x-((2*7^(1/2)+2)/4)))/(3*x^-1-1) = 0

((x-((2-2*7^(1/2))/4))*(x-((2*7^(1/2)+2)/4)))/(3*x^-1-1) = 0 // * 3*x^-1-1

(x-((2-2*7^(1/2))/4))*(x-((2*7^(1/2)+2)/4)) = 0

( x-((2*7^(1/2)+2)/4) )

x-((2*7^(1/2)+2)/4) = 0 // + (2*7^(1/2)+2)/4

x = (2*7^(1/2)+2)/4

( x-((2-2*7^(1/2))/4) )

x-((2-2*7^(1/2))/4) = 0 // + (2-2*7^(1/2))/4

x = (2-2*7^(1/2))/4

x in { (2-2*7^(1/2))/4} 

x = (2*7^(1/2)+2)/4

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