SOLUTION: For all positive numbers a and b, a function f satisfies the equation f (a b) = f(a) + f(b). if f(2) = x and f(5) = y, what is the value of f(100), in terms of x and y?

Algebra ->  Functions -> SOLUTION: For all positive numbers a and b, a function f satisfies the equation f (a b) = f(a) + f(b). if f(2) = x and f(5) = y, what is the value of f(100), in terms of x and y?       Log On


   

Question 527405: For all positive numbers a and b, a function f satisfies the equation f (a b) = f(a) + f(b). if f(2) = x and f(5) = y, what is the value of f(100), in terms of x and y?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
f(100) = f(10) + f(10) = (f(2) + f(5)) + (f(2) + f(5)). Replace f(2) with x and f(5) with y to obtain

f(100) = 2x + 2y.