How can two different utility functions represent the same preferences?
First of all, an utility function $u: X \rightarrow \mathbb{R}$ represents the preference relation $\succsim$ if: $$\forall a, b \in X, \; u(a) \geq u(b) \iff a \succsim b.$$

Well, if another function $v: X \rightarrow \mathbb{R}$ represents $\succsim$, then: $$\forall a, b \in X, \; v(a) \geq v(b) \iff a \succsim b.$$

But the above implies the following: 

$$\forall a, b \in X, \; u(a) \geq u(b) \iff v(a) \geq v(b).$$

Which means that both functions preserves the order relation, just as Herr K. said it. Another important part of Wikipedia's article is this one. You see, any monotonically increasing (and it must be increasing, not nondecreasing) function preserves the preference relation. 

So now I think you will be able to answer both questions. As a tip for the first one, think about the $\ln(x)$ function: is it a monotonic increasing function?