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Can you explain me why this is also isomorphism?

  1. Dec 19, 2012 #1
    Homomorphism is defined by ##f(x*y)=f(x)\cdot f(y)##. One interesting example of this is logarithm function ##log(xy)=\log x+\log y##. Can you explain me why this is also isomorphism?
     
    Last edited by a moderator: Feb 4, 2013
  2. jcsd
  3. Dec 19, 2012 #2

    tiny-tim

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  4. Dec 19, 2012 #3
    Re: Isomorphism

    I know that. But I asked only for logarithm because
    [tex]\log (ab)=\log (a)+\log (b)[/tex]
    [tex]\log ((-a)(-b))=\log (a)+\log (b)[/tex]
    Why function ##f(x)=e^x## isn't surjective?
     
  5. Dec 19, 2012 #4

    tiny-tim

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  6. Dec 19, 2012 #5
    Re: Isomorphism

    Ok. Tnx for the answer.
     
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