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Prove that 8(x) = eX defines an isomorphism of the group lII. of all real numbers
Chapter 18, Problem 18.11(choose chapter or problem)
Prove that 8(x) = eX defines an isomorphism of the group lII. of all real numbers (operationaddition) onto the group lII. P of all positive real numbers (operation multiplication). What isthe inverse of the mapping 8? Is the inverse an isomorphism?
Questions & Answers
QUESTION:
Prove that 8(x) = eX defines an isomorphism of the group lII. of all real numbers (operationaddition) onto the group lII. P of all positive real numbers (operation multiplication). What isthe inverse of the mapping 8? Is the inverse an isomorphism?
ANSWER:Step 1 of 3
Consider the function .
The objective is to determine that the is the bijection and the group homomorphism.
Let then, from the exponential of sum and the real number.