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

Question

how do you solve this problem?

Answer 1

 

 Using ln A/B = LnA - Ln B

 

    ln ( X+3) - ln ( X-1) =  ln e²

 

      Ln ( X+3)/ ( X -1) = ln e²

 

           (X+3) / (X -1 ) = e²

 

             X + 3 = e²( X -1) = e² X - e²

         

              X ( 1- e² ) = -3 - e²

            

               X = ( e² +3 ) / ( e²  - 1) = 1.63

 

                

         

Answer 2

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

So, x+3 = (x-1)e^2

Solve for x,

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