Is there any real-valued function, f, which is not a logarithm, such that ∀x,y in ℝ , f(x∗y)=f(x)+f(y)?
So far, all I can think of is z where z(x)=0 ∀x in ℝ
EDIT:
Functions having a domain of ℝ+ or a domain of ℝ/{0} are acceptable as well.
What are examples of functions, f, from ℝ/{0} to ℝ which are not logarithms, such that
∀x,y in ℝ, f(x∗y)=f(x)+f(y)?
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