Answer: X=14
please note that: 3^(a+b) = (3^a) * (3^b)

In the given question: x = (x-1) + 1

hence: 3^x = 3^(x-1)*3^1 = 3^(x-1)*3 [because 3^1 = 3]

Let me know if you have any questions. Thanks.

3^(x-1)[3-1]=3^13[2]

x-1=13; x=14

Sorry Bharat but the answer is 14.

OV25, could you detail your solution step by step please?

Thank you.

Yes zachthegnome you are correct. My bad for the typographical error. I have corrected my response above.

Here are the steps:

(3^x)-(3^(x-1)) = ((3)^13)(2)
Left side:
(3^x)-(3^(x-1))
= (3^(x-1))*3 - 3^(x-1)
= 3^(x-1)*(3 - 1) <take 3^(x-1) common>
= 3^(x-1)*(2)
Compare this with the right side:
x-1 = 13
hence x = 14.

Let me know if any questions. Thanks.

I think I follow now. I was initially confused between these two steps:
(3^x)-(3^(x-1))
= (3^(x-1))*3 - 3^(x-1)

Now correct me if I am wrong but you are able to transform (3^x) into (3^(x-1))*3 because the 3 implies 3^1 which by factoring out (I'll call it dividing out because that's the line of thinking that I am using) subtracts the 1 from the x.

Am I getting there?

Yes you are correct.

yes you got it zach.

Hey Zach,

Perfect explanation of what you did on this one - very nicely done!

The presence of subtraction in this problem is what really screws with people, I think - if it were:

3^(y+2) - (3^y)

It would probably seem more natural to factor out the 3^y from both because you can break out the first term into 3^y and 3^2:

3^y * 3^2 - 3^y

3^y ( 3^2 - 1)

Addition just makes more sense to people than does subtraction.

If you do find yourself in this situation, you can always rely on the fact that addition and subtraction are the exact same operation. You could take the problem as written:

3^x - 3^(x-1)

And do the same thing, just that the second term is the one that has two operations to it - the 3^x and then the "addition" of -1:

3^x - 3^x * 3^-1

Note that the second term, if you just combine the two exponents by adding, becomes x - 1.

This question is just a great example of how the GMAT likes to add difficulty. The way it's written isn't really "harder" than the example I gave with y (and just straight addition instead of subtraction), but it's certainly "less convenient". When you get into a situation like this, I think it really helps to take a deep breath and reframe the statement:

"It's subtraction of exponents - how do I get this to look like something I know how to do?"