Question

if n is a positive integer and k+2=3^n, which of the following could not be a value of k?
A 1
B 4
C 7
D 5
E 25

Answer 1

3 is odd. 3^n is odd for all values of n>0
k+2 is odd if k is odd, and k+2 is even if k is even.

Answer 2

To me, I rather test one by one from the option than follow that rule.
counterexample: 9 is odd, but 9+2 =11 and there is no n satisfy 3^n =11.

Answer 3

As long as we know that the right-hand side (3^n) is always odd, the rest could be solved by inspection.