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)

Question

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)

anonymous · Answer

Try them and see?

anonymous · Answer

$$f(x) = \frac{1}{x}\implies $$
$$f(ab) = \frac{1}{ab}$$
$$f(a) + f(b) = \frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab}$$
$$\implies f(ab) \ne f(a)+f(b)$$

Nope, not that one.

anonymous · Answer

Which one are you going to try next?

anonymous · Answer

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?

anonymous · Answer

Right.

anonymous · Answer

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!!

anonymous · Answer

Yes, but cause the sum of logs is the log of the product.

anonymous · Answer

err because rather.

anonymous · Answer

$$log(a) + log(b) = log(a*b)$$