## anonymous 5 years ago 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)

1. anonymous

Try them and see?

2. anonymous

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

3. anonymous

Which one are you going to try next?

4. anonymous

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?

5. anonymous

Right.

6. anonymous

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!!

7. anonymous

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

8. anonymous

err because rather.

9. anonymous

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