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Continuity homework problem

  1. Apr 12, 2010 #1
    how can we prove that lun x is continuous over (0, [tex]\infty[/tex] )?

    Provided that we define : lun x =y <=> [tex]e^y =x[/tex]?
     
  2. jcsd
  3. Apr 12, 2010 #2

    mathman

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    Re: continuity

    lnx - lnu = ln(x/u). For any fixed x > 0, u->x => x/u -> 1 and ln1=0.

    You can dress this proof up.
     
  4. Apr 12, 2010 #3
    Re: continuity

    Can you elaborate a little more ? I do not how to start
     
  5. Apr 13, 2010 #4

    mathman

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    Re: continuity

    I am not sure what you are given to start with. For example are you assuming ey is continuous? My proof (I admit) is somewhat flawed. It needs continuity of ln(x) for x=1, which then implies continuity for all x.
     
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