f(ab)=f(a) + f(b) for all real numbers in the domain of f, f(x) equals which of these? (A)1/x (B) e^x (C) log(x)

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f(ab)=f(a) + f(b) for all real numbers in the domain of f, f(x) equals which of these? (A)1/x (B) e^x (C) log(x)

Mathematics
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\[f(x) = \frac{1}{x}\implies \] \[f(ab) = \frac{1}{ab}\] \[f(a) + f(b) = \frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab}\] \[\implies f(ab) \ne f(a)+f(b)\] Nope, not that one.
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would this process be right? ::: f(x)= e^x f(ab)= e^ab f(a)+f(b)= e^a +e^b which does not equal e^ab ?? yes?
Right.
ohh~~ so it's the third choice! i see it now...i did log 5 + log 2 and then it came as one which is the same as log 5*2. i get it now. THANKS!!
Yes, but cause the sum of logs is the log of the product.
err because rather.
\[log(a) + log(b) = log(a*b)\]

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