Question: Consider the vector space R+ where vector addition and scalar multiplication are not the ones inherited from R but rather are these: a + b

Consider the vector space R+ where vector addition and scalar multiplication are not the ones inherited from R but rather are these: a + b is the product of a and b, and r a is the r-th power of a. (This was shown to be a vector space in an earlier exercise.) Verify that the natural logarithm map ln: R+ → R is a homomorphism between these two spaces. Is it an isomorphism?

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