At the point of interception of this graph, a=b=0 and the value of the function 2^a=3^b=1.
If you draw lines parallel to the X axis, you can see that different values for a and b can lead to the same y. There are other pairs (a,b) such that 2^a=3^b.

To say it in a more mathematical way:
Lets denote two functions f(x)=2^x and g(x)=3^x
at the point of interception f(0)=g(0)=1.
Howerver, there are other pairs (a,b) such that f(a)=g(b)\neq1. So there are other soulution for f(x)=g(x) other than (a,b) = (0,0)

Oh, hand't seen LenaA's explanation. Oustanding.

2^ln(3) = 2.141486064 = 3^ln(2)

Answer is C
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Please kudos if my post helps.

Yeah, so I think the answer should be E.

The slopes will tell us nothing about whether both lines are parallel or equal. Additional information about the Y-intercept is missing.
So, a vote for E.

The GMAT Exam won't necessarily use logarithms on the exam as this is generally understood as more advanced math. But the question itself does not use any logarithms - it's merely an expression with variables in the exponent.

For the purposes of understanding the expression further it may help to do basic logs (in this case, take the log of both sides). So you should brush up on the basics here so you can better rearrange equations when there is a need. There may certainly be other ways to approach the problem rather than do some basic logs (ie randomly input numbers for x and y and see what results you get) but you are better off learning the basics of logs here.

The issue here among everyone is whether 2 lines with the same slope are parallel. And the answer here is -- for most the part.
This is where the GMAT test takers get tricky and even when you think you understand a concept, you may still get it wrong.

Parallel lines satisfy BOTH of the following:
1) Same slope - yes, this happens when we combine both statements and have a=b=0
2) Don't touch each other. Or in math terms, can draw a perpendicular line to each other, create interior angles of 90 degrees, and never cross.

So when we have two lines with the same slope, they are parallel except when they are the same line. So don't jump to answer choices right away when you follow the rule of thumb (parallel lines = same slope). You really have to think about all scenarios when it comes down to these data sufficiency problems.
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From your comment above I conclude that E is the right answer for this Question.