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|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

Basically you take the equation above, and remove 2^x out of the equation It's like saying x^2 - xy to x(x-y)

SO it can also be written as (2^x)(2^2) - (2^x)(1) which then becomes (2^x)(2^2 - 1)

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Basically you take the equation above, and remove 2^x out of the equation It's like saying x^2 - xy to x(x-y)

SO it can also be written as (2^x)(2^2) - (2^x)(1) which then becomes (2^x)(2^2 - 1)

Hope that was helpful, I'm a GMAT instructor for Manhattan Review. If you would like help preparing for your GMAT, feel free to look us up.

______________________ Manhattan Review Unlimited GMAT Class Hours & MBA Admissions +1 212 997 1660 | Singapore: +65 3106 2069 / +65 9686 8794 10% discount on all services for GMAT Club members

A simple factorization! I was confused as i thought (2^x)(2^2 - 1) was (2^x)(2^2-1)

Simplifying the right side, 3 * 2^13 (2^2 - 1) * 2^13 2^2*2^13 - 2^13 (Multiplying with both terms inside) 2^15 - 2^13 (adding the powers since base is same)

=> 2^x - 2^ (x - 2) = 2^15 - 2^13 => Hence, x = 15 or x - 2 = 13, x = 15.

This has always been a favorite problem of mine - the first time I saw it, an instructor had blanked on how to solve it and emailed me a photo from his phone asking for help. He had excused himself from a tutoring session and needed me to explain how to solve it (correctly, of course) within a few minutes, so the pressure was on!

Bunuel's explanation is perfect (as always), but when the pressure was on and I wasn't exactly thinking about factoring, I did this instead - I looked to see if there were a pattern in the subtraction at left (2 to an exponent minus 2 to another exponent, two less) that would always produce 3*something on the right. So I did:

x = 3 and x-2 = 1 2^3 - 2^1 = 8 - 2 = 6

And 6 = 3(2^1), so I had a start.

x = 4 and x-2 = 2 2^4 - 2^2 = 16 - 4 = 12

And 12 = 3(2^2), so the pattern held

x = 5 and x-2 = 3 2^5 - 2^3 = 32 - 8 = 24

And 24 = 3(2^3), and the pattern became clear... The operation at left was always producing 3*2^(x-2) as its answer, so if x-2 = 13, then x = 15.

Strategically, using small numbers to establish patterns works pretty well when huge numbers (like 3(2^13)) are in play, and when exponents are involved (exponents are essentially just repetitive multiplication, so there are bound to be some repetitive patterns involved). If you can factor like Bunuel did, that's a great way to go...but I'd recommend having the "prove patterns w/ small numers" ideology in your arsenal!
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I am having trouble understanding this... I can't remember whose notes this is from, but it is something I printed off this site.

7^4 + 7^7 = 7^4(1+7^3) =7^4(50)

And

3^4+12^4 =3^4+ (3*4)^4 =3^4(1+4^4) =3^4(256)

In both instances I am confused with what happens to the one in the second to last step. Wouldn't it be 3^4+3^4(256)? It seems like the 1 just disappears???

Here is a problem I can not solve:

2^x - 2^x-2 = 3(2^13)

x=?

The answer is 15 but I do not understand how to get it. Is there a good guide online or does someone have good notes for exponents? I am lacking in this area and I need it dumbed down.

So please: Provide answer choices for PS questions. Make sure you type the question in exactly as it was stated from the source.

About the examples: 1. \(7^4+7^7\) --> factor out 7^4 --> \(7^4(1+7^3)=7^4(1+343)=7^4*344\) (so the answer given in your example is not correct);

2. \(3^4+12^4=3^4+(3*4)^4=3^4+3^4*4^4\) --> factor out 3^4 --> \(3^4(1+4^4)=3^4(1+256)=3^4*257\) (so again the answer given in your example is not correct).

The question itself: If 2^x - 2^(x-2) = 3*2^13, what is the value of x? A. 9 B. 11 C. 13 D. 15 E. 17

Re: If 2^x - 2^(x-2) = 3*2^13, What is the value of x? [#permalink]

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09 Jun 2012, 00:44

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This has the look of not factoring easily, so I applied some logic first.

We can rule out A,B and C (as the left hand side would all be 2^13 less a positive number (smaller than 2^13), so could never equal 3 * 2^13 (larger than 2^13)

Re: If 2^x - 2^(x-2) = 3*2^(13), what is x? [#permalink]

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28 Aug 2013, 14:27

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I did it a bit differently, but I arrived at the right answer. Here is the way I did it: \(2^x - 2^{x-2} = 3* 2^{13}\) Factor out a \(2^x\) which gives: \(2^x(1 - \frac{1}{4}) = 3* 2^{13}\) Clean up: \(2^x(\frac{3}{4}) = 3* 2^{13}\) At this point I realized that the 4 in the denominator could be factored out so that's what I did: \(2^{x-2}(3) = 3* 2^{13}\) From here you have \(2^{x-2} = 2^{13}\) so \(x = 15\)

I hope that helps.
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Can you please explain the red highlighted part? I read other explanations but it wasn't clear. I am unable to understand how did you factor out 2^(x-2)?

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