Solution Found!

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)

Get Unlimited 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?

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.

                                                                   

 

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back