MHB Given f(xy) = f(x)/y and f(500) = 3, find f(600)

[mathtopamela]

Help me understand the following problem:

Let f be a function satisfying f(xy) = f(x)/y for all positive real numbers x and y, and f(500) = 3.
What is f(600)?

 

[kaliprasad]

Help me understand the following problem:

Let f be a function satisfying f(xy) = f(x)/y for all positive real numbers x and y, and f(500) = 3.
What is f(600)?

you are given f(500) = 3 or

x = 500, f(x) = 3

you need to calculate f(600) or xy = 600.

you can now calculate the value of y and then f(xy) or f(600)

 

[HallsofIvy]

600= 500(6/5) so f(600)= f(500(6/5)). (x= 500, y= 6/5)