SOLUTION: A function f(n) defined for all positive integers has the property that f(m) + f(n) = f(mn) for any two positive integers m and n. if f(2)= 7 and f(3)=10, then calculate f(12).

Algebra ->  Functions -> SOLUTION: A function f(n) defined for all positive integers has the property that f(m) + f(n) = f(mn) for any two positive integers m and n. if f(2)= 7 and f(3)=10, then calculate f(12).      Log On


   

Question 80206: A function f(n) defined for all positive integers has the property that f(m) + f(n) = f(mn) for any two positive integers m and n. if f(2)= 7 and f(3)=10, then calculate f(12).
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

A function f(n) defined for all positive integers
has the property that f(m) + f(n) = f(mn) for any 
two positive integers m and n.  if f(2)= 7 and 
f(3)=10, then calculate f(12).

f(12) = f(4·3) = f(4) + f(3) = f(4) + 10 = 

f(2·2) + 10 = [f(2) + f(2)] + 10 = [7 + 7] + 10 =

14 + 10 = 24.

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Another way:

f(12) = f(2·6) = f(2) + f(6) = 7 + f(6) = 7 + f(2·3) =

7 + [f(2) + f(3)] = 7 + [7 + 10] = 7 + 17 = 24. 

Edwin