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If 2^x-2^(x-2)=3*2^13 what is the value of x?

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If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 02 Apr 2012, 13:05
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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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 02 Apr 2012, 17:04, edited 1 time in total.
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Re: Value of X [#permalink] New post 02 Apr 2012, 17:04
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enigma123 wrote:
If 2^x - 2^x ^ - ^2 = 3 (2^1^3) What is the value of x?

A) 9

B) 11

C) 13

D) 15

E) 17


Question should read;

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

2^x-2^{x-2}=3*2^{13} --> 2^x-2^{x}*2^{-2}=3*2^{13} --> 2^x-\frac{2^{x}}{2^{2}}=3*2^{13} --> 2^x(1-\frac{1}{2^{2}})=3*2^{13} --> 2^x*\frac{3}{2^{2}}=3*2^{13} --> 2^x=2^{15} --> x=15.

Answer: D.
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 03 Apr 2012, 06:09
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enigma123 wrote:
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



tricky....we would fall for 13...but answer is x-2=13 so x=15 i.e D
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Re: Value of X [#permalink] New post 04 Apr 2013, 23:50
Bunuel wrote:
2^x(1-\frac{1}{2^{2}})=3*2^{13} --> 2^x*\frac{3}{2^{2}}=3*2^{13}.



Bunuel, can you tell me what you did in these steps? Where does the 3 come from?
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 05 Apr 2013, 01:45
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I can explain that:

2^x-2^x^-^2=2^x(1-2^-^2)=2^x(1-\frac{1}{2^2})=\frac{2^x*3}{4}=3*2^1^3
divide by 3
\frac{2^x}{4}=2^1^3=2^x^-^2=2^1^3

Hope now it's clear
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 05 Apr 2013, 05:06
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enigma123 wrote:
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


Just another way of doing this sum:
2^x-2^{x-2}= (4-1)*2^{13}

or 2^x-2^{x-2} = 2^{15}-2^{13}

Thus, x = 15.
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 06 Apr 2013, 05:45
2^x - 2^(x-2) = {2^(x-2)} * ( 2^2 - 1) = {2^(x-2)} * 3 = 3 * 2^13
--> 2^(x-2) = 2^13
--> x-2 = 13
--> x = 15
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 23 Jul 2013, 09:18
Zarrolou wrote:
I can explain that:

2^x-2^x^-^2=2^x(1-2^-^2)=2^x(1-\frac{1}{2^2})=\frac{2^x*3}{4}=3*2^1^3



Hey ! Unfortunately, I still don't get where that '3' comes from... Just don't see it... Could anyone explain further in more detail?! Would be great!
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 23 Jul 2013, 09:24
Expert's post
TheGerman wrote:
Zarrolou wrote:
I can explain that:

2^x-2^x^-^2=2^x(1-2^-^2)=2^x(1-\frac{1}{2^2})=\frac{2^x*3}{4}=3*2^1^3



Hey ! Unfortunately, I still don't get where that '3' comes from... Just don't see it... Could anyone explain further in more detail?! Would be great!


Step by step:
2^x-2^{x-2}=3*2^{13}

2^x-2^{x}*2^{-2}=3*2^{13}

2^x-\frac{2^{x}}{2^{2}}=3*2^{13}

2^x(1-\frac{1}{2^{2}})=3*2^{13}

2^x(\frac{2^2-1}{2^{2}})=3*2^{13}

2^x*\frac{3}{2^{2}}=3*2^{13}

2^x=2^{15}

x=15.

Hope it's clear.
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 23 Jul 2013, 10:51
Bunuel wrote:

Step by step:


2^x(1-\frac{1}{2^{2}})=3*2^{13}

2^x(\frac{2^2-1}{2^{2}})=3*2^{13}



Hey, now its clear where the 3 comes from but how did u get the 2^2 there? Sry, was a long day... I bet its easy as hell but I'm just confused atm.. :?
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 23 Jul 2013, 11:38
Expert's post
TheGerman wrote:
Bunuel wrote:

Step by step:


2^x(1-\frac{1}{2^{2}})=3*2^{13}

2^x(\frac{2^2-1}{2^{2}})=3*2^{13}



Hey, now its clear where the 3 comes from but how did u get the 2^2 there? Sry, was a long day... I bet its easy as hell but I'm just confused atm.. :?


I think you should brush up fundamentals:

2^{-2}=\frac{1}{2^2}.
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 23 Jul 2013, 11:41
Hey, that I understand... but how did u get the 2^2 onto the fraction again to get 2^2-1/2^2 ? I must miss something very fundamental indeed..
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 23 Jul 2013, 11:43
Expert's post
TheGerman wrote:
Hey, that I understand... but how did u get the 2^2 onto the fraction again to get 2^2-1/2^2 ? I must miss something very fundamental indeed..


Can you please tell me what didn't you understand below?

2^x-2^{x-2}=3*2^{13}

2^x-2^{x}*2^{-2}=3*2^{13}

2^x-\frac{2^{x}}{2^{2}}=3*2^{13}
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 23 Jul 2013, 11:49
Bunuel wrote:

Can you please tell me what didn't you understand below?

2^x-2^{x-2}=3*2^{13}

2^x-2^{x}*2^{-2}=3*2^{13}

2^x-\frac{2^{x}}{2^{2}}=3*2^{13}


Hey, sry for not getting it. In the extract shown above I understand everything.

What I seem to not get is how you got from 2^x (1-1/2^2) to 2^x (2^2-1/2^2).

Oh wait... did u just multiply with the common denominator (2^2*(-1)) ?
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 23 Jul 2013, 11:57
1
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TheGerman wrote:
Bunuel wrote:

Can you please tell me what didn't you understand below?

2^x-2^{x-2}=3*2^{13}

2^x-2^{x}*2^{-2}=3*2^{13}

2^x-\frac{2^{x}}{2^{2}}=3*2^{13}


Hey, sry for not getting it. In the extract shown above I understand everything.

What I seem to not get is how you got from 2^x (1-1/2^2) to 2^x (2^2-1/2^2).

Oh wait... did u just multiply with the common denominator (2^2*(-1)) ?


1-\frac{1}{2^{2}} --> \frac{2^2}{2^2}-\frac{1}{2^{2}} --> \frac{2^2-1}{2^{2}}
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Gmat prep exam exponent question [#permalink] New post 06 Oct 2013, 13:11
Hello Everyone,

While completing the GMAT prep exam I stumbled upon a problem solving question that am not able to crack and I am seeking for some advice/pointers on this question:

If 2^x - 2^x-2 = 3(2^13) what is x?

It would be easier to solve if the 3 was not included in the equation at all but of course nothing about the gmat is easy.

Am not looking for the answer just pointers. I did review the exponent rules from the MGMAT Number Properties guide but according to the rule for a * b^ This kind of expression can not be simplified any further so it's kind of confusing,

Thanks for your help in advance
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Re: Gmat prep exam exponent question [#permalink] New post 06 Oct 2013, 13:14
Expert's post
dilevbare1 wrote:
Hello Everyone,

While completing the GMAT prep exam I stumbled upon a problem solving question that am not able to crack and I am seeking for some advice/pointers on this question:

If 2^x - 2^x-2 = 3(2^13) what is x?

It would be easier to solve if the 3 was not included in the equation at all but of course nothing about the gmat is easy.

Am not looking for the answer just pointers. I did review the exponent rules from the MGMAT Number Properties guide but according to the rule for a * b^ This kind of expression can not be simplified any further so it's kind of confusing,

Thanks for your help in advance


Merging similar topics. Please refer to the solutions above.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules 1, 3, 7, and 8. Thank you.
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If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 26 Feb 2014, 19:31
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One more method:

2^x - 2^{(x-2)} = 3 * 2^{13}

2^x - 2^{(x-2)} = ( 4-1 ) * 2^{13}

2^x - 2^{(x-2)} = 4 * 2^{13} - 1 * 2^{13}

2^x - 2^{(x-2)} = 2^{15} - 2^{13}

Comparing both sides, we get x = 15 = Answer = D


What I like about this method is we need not have to expand/solve the LHS of the equation. Just adjust 3 of the RHS as (4-1) & it does the trick
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Last edited by PareshGmat on 27 Oct 2014, 20:30, edited 2 times in total.
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 18 Aug 2014, 04:54
Has anyone encountered a problem similar to this? Maybe there is a collection of similar problems floating around somewhere? Thanks!
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] New post 18 Aug 2014, 05:58
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Has anyone encountered a problem similar to this? Maybe there is a collection of similar problems floating around somewhere? Thanks!


DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
PS Exponents questions to practice: search.php?search_id=tag&tag_id=60
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x?   [#permalink] 18 Aug 2014, 05:58
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Median: What is value of X humans 4 24 Jun 2006, 02:06
What is the value of x? remgeo 2 08 May 2006, 06:38
What is the value of │x + 7│? M8 7 05 May 2006, 19:46
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If 2^x-2^(x-2)=3*2^13 what is the value of x?

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