Let G = {x E R |x>0 and x 1}, and define * on G by a * b= a lnb for all a, b E G Prove that the group (G, *) is isomorphic to the group R* under the standard multiplication.

Let G = {x E R |x>0 and x 1}, and define * on G by a * b= a lnb for all a, b E G Prove that the group (G, ) is isomorphic to the group R under the standard multiplication.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 28E

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Let G = {x E R|x>0 and x ± 1}, and define * on G by a * b
= a In b for all a, b E G
Prove that the group (G, *) is isomorphic to the group R* under the standard multiplication.

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