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Solve for x of an exponential function

  1. Dec 2, 2008 #1
    1. The problem statement, all variables and given/known data

    e^(2x+9) - 4e^x -5 = 0

    2. Relevant equations



    3. The attempt at a solution
    I changed this into: e^(2x+9) =4e^x + 5
    I took logarithm of both sides:
    2x+9=ln(4e^x +5)

    but i dont know what to do with the right hand side.
    what will be the easiest way to solve this?
    Thank you very much
     
  2. jcsd
  3. Dec 2, 2008 #2
    Try this,
    [tex]\begin{align*}
    0 & = e^{ 2 x + 9 } - 4 e^x - 5 \\
    & = e^9 e^{ 2 x } - 4 e^x - 5.
    \end{align*}[/tex]

    Then the substitution [tex]u=e^x[/tex] turns this into a quadratic equation, which is easily solved, and then [tex]x = \ln u[/tex].
     
  4. Dec 2, 2008 #3
    excellent.
    thank you v much
     
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