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using theorem 11.10 (First Isomorphism Theorem), Show that the set of positive real numbers with multiplication...

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Advance Math

using theorem 11.10 (First Isomorphism Theorem), Show that theset of positive real numbers with multiplication is isomorphic tothe set of real numbers with addition.

Theorem 11.10 First Isomorphism Theorem. If ψ : G → H is a grouphomomorphism with K = kerψ, then K is normal in G. Let ϕ : G → G/Kbe the canonical homomorphism. Then there exists a uniqueisomorphism η : G/K → ψ(G) such that ψ = ηϕ.

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