I have to show that the function Ø gives the isomorphism of G with G', by showing that Ø is a one to one function and is onto G'.

From my notes,

(1) if xØ = yØ, then e^x= e^y, so x=y. thus Ø is one to one.

(2) if r in R+, then

(In r)Ø = e ^ (In r) = r

where ( In r ) in R. thus Ø is onto R+.

why does (1) and (2) prove that Ø is one to one and is onto?

thanks!