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Solving log equation

  1. Jul 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Do anyone know how to solve:
    y=LN x
    y=e+1-x


    2. Relevant equations


    y=LN x
    y=e+1-x



    3. The attempt at a solution

    LN x=e+1-x
    x=e^e * e^1 / e^x
    x*e^x=e^(e+1)

    then I dont know how to solve, must I solve it graphically?

    Actually, the original question is :
    Double integration
    InIn x dxdy for the area bounded by y=e+1-x and y=LNx and x-axis
     
  2. jcsd
  3. Jul 18, 2012 #2
    Trial and error shows [itex]x = e[/itex] is a solution to [itex]\ln{x} = e + 1 - x[/itex]. Closer inspection reveals the solution is unique because [itex]\ln{x}[/itex] is strictly increasing while [itex]e + 1 - x[/itex] is strictly decreasing.

    I know not of an elementary technique for solving such an equation.
     
  4. Jul 18, 2012 #3
    Thanks a lot.
     
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