Crasher,
The key to your question from GMATprep is to recognize that because your variable appears within an exponent on base 2, you need to "create" a 3 somewhere on the left side of the equation. That way, you'll be able to cancel the 3s and compare the exponents of like bases.
You must also recognize the rule of exponents that (2^X)(2^Y) = 2^(X+Y) ... to help you remember that, recall that two squared times two squared is simply "two times two times two times two" or two to the fourth.
[apologies for spelling out the powers, y'all, I think it's often easier than using carrots to denote superscript].
Now ... with this problem, is there something you can factor out of the left side that will result in a 3 multiplied by a power of 2?? Answer follows as a spoiler, for anybody that wants to try it!
[spoiler]
If you factor 2^(X-2) out of the left side, you end up with [2^(X-2)](2^2 + 1) or 3[2^(X-2)]. The threes cancel, and that allows you to set the exponents equal. X-2 = 13 ... and you can take it from there![/spoiler]
Hope that helps! Steve
Stephen
GMAT Instructor
Knewton Inc.
