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?

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.Com

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) (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.
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