F(x)+f(y)=f(xy) what f(x)=??

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Jan 18, 2018

Answer:

See below.

Explanation:

This is the famous #log# function

#f(x)+f(1)=f(x) rArr f(1) = 0#

now

#{(2f(x) = f(x^2)), (f(x) = f(x)):}#

adding both sides

#3f(x) = f(x^2)+f(x) = f(x^3) rArr mf(x) = f(x^m)# etc.

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