Function problem?

[e^x]

Full Question: Define f(x) to be the largest number such that 2 raised to the number is a divisor of x. If f(n) = 4, what is f(2n + 24)?

What I've done:
2^4=16

n/16=1
n=16

f(2n+24)=f(56)

56/2^f(56)=1
56=2^f(56)

Since 2 raised to any non decimal power isn't 56, I'm stuck.

 

[Dr.Peterson]

Full Question: Define f(x) to be the largest number such that 2 raised to the number is a divisor of x. If f(n) = 4, what is f(2n + 24)?

What I've done:
2^4=16

n/16=1
n=16

f(2n+24)=f(56)

56/2^f(56)=1
56=2^f(56)

Since 2 raised to any non decimal power isn't 56, I'm stuck.

You don't know that n is 16; but you do know that 16 is a divisor of 16. What power of 2 can be a divisor of 2n + 24?