# Can you explain me why this is also isomorphism?

1. Dec 19, 2012

### matematikuvol

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. Dec 19, 2012

### tiny-tim

3. Dec 19, 2012

### matematikuvol

Re: Isomorphism

I know that. But I asked only for logarithm because
$$\log (ab)=\log (a)+\log (b)$$
$$\log ((-a)(-b))=\log (a)+\log (b)$$
Why function $f(x)=e^x$ isn't surjective?

4. Dec 19, 2012

### tiny-tim

5. Dec 19, 2012

### matematikuvol

Re: Isomorphism

Ok. Tnx for the answer.

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