Trying to figure out this problem. But, I think my log abilities are betraying me:

Determine whether the following is true or false. If true justify your answer by finding constants C and K. If the statement is false, supply a counter example:

n^n is O(2^n)

I set n^n <= 2^n

ln (n^n) <= ln(2^n)

n ln(n) <= n ln(2)

n <= ln(2)

This doesn't seem correct. Any ideas?