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

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Question Stats: 80% (01:29) correct 20% (01:44) wrong based on 580 sessions

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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

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Originally posted by enigma123 on 02 Apr 2012, 14:05.
Last edited by Bunuel on 28 Mar 2016, 02:02, edited 2 times in total.
Edited the question
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x?  [#permalink]

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22
15
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]

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63
10
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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Kindly press "+1 Kudos" to appreciate Originally posted by PareshGmat on 26 Feb 2014, 20:31.
Last edited by PareshGmat on 27 Oct 2014, 21:30, 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]

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1
1
1
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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GMAT 1: 700 Q44 V42 Re: If 2^x-2^(x-2)=3*2^13 what is the value of x?  [#permalink]

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2
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]

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4
1
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]

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10
3
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]

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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]

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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]

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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]

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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]

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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]

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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]

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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]

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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]

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1
1
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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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x?  [#permalink]

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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]

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JackSparr0w wrote:
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]

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Hello everyone,

this question came up as one of the early ones in my gmat prep exam (scored very badly). Is this really a sub-600 question?

I always have struggles with those questions (exponents, roots), but I DO REALLY understand the explanation. However, as soon as I come across a similar problem, I never know how to approach it correctly.. Does anyone have some tips? I already practiced a lot of similar problems, but it's seems that I am still not improving.
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x?  [#permalink]

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Do you keep your work? If so, at which step did you mess up? Also, make sure you can verbally explain why you did each step. Re: If 2^x-2^(x-2)=3*2^13 what is the value of x?   [#permalink] 28 Oct 2014, 10:54

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