- #1

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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?

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- Thread starter matematikuvol
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- #1

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- #2

tiny-tim

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an isomorphism is a homomorphism that is bijective (one-to-one and onto)

(see http://en.wikipedia.org/wiki/Isomorphism)

- #3

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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?

- #4

tiny-tim

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(see also http://en.wikipedia.org/wiki/Isomorphism#Practical_examples)

- #5

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Ok. Tnx for the answer.

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