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Exponential function

  1. Oct 11, 2011 #1
    f(x)= lnx ; g(x) = ex

    f{g(x)} = ln ex = x; not an issue

    g{f(x)}= eln x = ???? (answer for this) f(x) and g(x) are inverse of each other.

    how to solve the problem algebraically.
     
  2. jcsd
  3. Oct 11, 2011 #2

    Hootenanny

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    You answered the question yourself:
     
  4. Oct 11, 2011 #3
    g{f(x)}= elnx = ???? how to solve this equation algebraically and come to a solution..
     
  5. Oct 11, 2011 #4

    micromass

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    What does it mean that f and g are inverses of eachother??
     
  6. Oct 11, 2011 #5
    I suggest trying to prove it for yourself first. If you really can't, I've "spoilered" a proof below. It sounds like you may want to go back and brush up on some of your fundamentals.

    [tex]y = e^{\ln x}[/tex]
    [tex]\ln y = \ln e^{\ln x}[/tex]
    [tex]\ln y = \ln x[/tex] (by the power rule of exponential functions, since ln e = 1)
    [tex]y=x=e^{\ln x}[/tex]
     
    Last edited: Oct 11, 2011
  7. Oct 11, 2011 #6
    OMG i was perfect till ln y = ln x; after that i confused myself over if ln y = ln x; does that imply y = x, now i can see the perfect picture, thanks very much for shedding light over the darkness my ignorance :)
     
    Last edited: Oct 11, 2011
  8. Oct 11, 2011 #7
    g{f(x)} = f{g(x)}, and both are one to one, hence inverse of each other.
     
  9. Oct 13, 2011 #8
    Algebraic Solution ??
    OK
    Let the solution be called "c"
    e^(Ln x) = c
    Take the Ln of both sides
    Ln [ e^(Ln x) ] = Ln c
    Use the Power Rule for Logs to get
    Ln x Ln e = Ln c
    but Ln e = 1 so
    Ln x = Ln c
    thus
    c = x
     
    Last edited: Oct 13, 2011
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