Monday, 24 March 2014

functional equations - Are there any real-valued functions, besides logarithms, for which f(xy)=f(x)+f(y)?

Is there any real-valued function, f, which is not a logarithm, such that x,y in , f(xy)=f(x)+f(y)?




So far, all I can think of is z where z(x)=0 x in



EDIT:



Functions having a domain of + or a domain of /{0} are acceptable as well.



What are examples of functions, f, from /{0} to which are not logarithms, such that
x,y in , f(xy)=f(x)+f(y)?

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