why the answer isnt B?

[diebeatsthegmat]

Q1 If 3^a*4^b = c, what is the value of b?

(1) 5^a = 25
(2) c = 36

[Anurag@Gurome]

Q1 If 3^a*4^b = c, what is the value of b?

(1) 5^a = 25
(2) c = 36

(1) 5^a = 25 implies 5^a = 5^2
Since the bases are the same, so exponents will also be equal. Hence, a = 2.
3^2 * 4^b = c does not give us the value of b until we know c; NOT sufficient.

(2) c = 36 implies 3^a * 4^b = 3^2 * 4^1 (as 36 = 3^2 * 4^1)
a = 2 and b = 1; SUFFICIENT.

The correct answer is B.

[gmatboost]

That is only the case if we assume that a and b must be integers.
Presumably that assumption is supposed to be part of this problem, but it's not stated.