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The Inverse of ln

  1. Feb 24, 2009 #1
    1. The problem statement, all variables and given/known data
    http://img5.imageshack.us/img5/2327/nummer1.jpg [Broken]


    2. Relevant equations

    5a: ln((x*(x-2))/(x2-4))
    ln((x22x)/(x2-4))
    ln(x/(x+2)) <-- the answer (i think)
    3. The attempt at a solution
    Im not completly sure about that answer in 5a so could somebody check that? also I'am having truble with b:

    f(x)--> y=ln(x/(x+2))
    f-1(x)--> x=ln(y/(y+2))
    ex=y/(y+2)

    then i get in truble...
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 24, 2009 #2

    HallsofIvy

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    [itex]x^2- 4= (x-2)(x+2)[/itex] and, as long as x is not equal to 2, you can cancel the two (x- 2) factors. But the original formula is not defined for x= 2 so, yes, that is equivalent to the original.

    Good, you are almost done. If you had A= y/(y+ 2) you could solve for y by multiplying on both sides by y+ 2 to get Ay+ 2A= y so (1- A)y= 2A and y= 2A/(1- A). Does that help?
     
    Last edited by a moderator: May 4, 2017
  4. Feb 24, 2009 #3
    ohh, i see!
    Then the answer is 2ex/(1-ex)
    You sir, are very helpful (wo?)man.:tongue2:
    Thanks a lot!
     
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