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

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


D( x )

x-1 <= 0

2*x+3 <= 0

x-1 <= 0

x-1 <= 0

x-1 <= 0 // + 1

x <= 1

2*x+3 <= 0

2*x+3 <= 0

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

2*x <= -3 // : 2

x <= -3/2

x in (1:+oo)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

x in { (1-(3*(-e^(1/2))))/(2*(-e^(1/2))+1)} 

x belongs to the empty set

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