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Solving logarithms

  1. Apr 11, 2004 #1
    Greetings all, I'm doing a refresh of calculus and physics in preparation for getting back to school this fall after a 5 year layoff. Most stuff is coming back pretty quickly, but I'm stuck on this one problem. I'm sure I'm missing something small, but I just haven't been able to find any example problems that match this one.

    g(x)=3+x+e^x
    g(x)=y

    I need to find the inverse of this function, which means solving for x. If I take the ln e^x to get x, I'm stuck on the other side with ln (y-3-x)=x I'm not sure where to go from here, any help would be greatly appreciated.
     
  2. jcsd
  3. Apr 11, 2004 #2

    HallsofIvy

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    Since g has x both "inside" and "outside" the exponential, its inverse is not any "elementary" function. Exactly what does the problem ask you to do?
     
  4. Apr 11, 2004 #3

    Zurtex

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    If your finding the root of the equation then you want to find x for:

    [tex]3 + x + e^x = 0[/tex]

    And I must say I'm a little stumped on how you would work out an exact answer.
     
  5. Apr 11, 2004 #4
    if g(x)=3+x+e^x Find g^-1(4)

    I'm reading this as "find the inverse g(x) function and then solve it when x=4" The answer in the back of the book shows that it should be 0.
     
    Last edited: Apr 11, 2004
  6. Apr 11, 2004 #5
    The inverse of g(x = 4) is 1/(7 + e4) though.
     
  7. Apr 11, 2004 #6

    matt grime

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    that isn't the inverse, that's the reciprocal.

    by inspection g(0) = 3+0+e^0 = 4,

    (technical note, g is monotone increasing so inverse is well defined)

    hence g^{-1}(4) = 0

    and similiarly g^{-1}(4+e) = 1
     
    Last edited: Apr 11, 2004
  8. Apr 11, 2004 #7
    Since it wasn't immediately apparent to me what matt was doing, here's a general point:

    For some function f(x),

    If:
    f(b)=a

    Then:
    f^{-1} (a) = b
     
  9. Apr 11, 2004 #8

    HallsofIvy

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    Yep. The problem did NOT ask that you actually find g-1(x),
    only that you find g-1(4).

    That is exactly the same as solving the equation 3+ x+ ex= 4 or
    x+ ex= 1. There is still no general way of solving an equation like that, but you might be as smart as Matt Grime and recognize that if x= 0, e0= 1 so
    0+ e0= 1. g-1(4)= 0.
     
  10. Apr 11, 2004 #9
    Thanks guys, after thinking about Matt's answer, I'm pretty sure that's what the problem was getting at.
     
  11. Aug 19, 2008 #10
    need help solving a problem can u help
     
  12. Aug 22, 2008 #11

    HallsofIvy

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    If you will post your problem in a new thread I am sure a lot of people can help.
     
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