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# If 2^x - 2^(x-2) = 3(2^13), what is the value of x? A) 9 B)

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Manager
Joined: 21 Mar 2007
Posts: 73
If 2^x - 2^(x-2) = 3(2^13), what is the value of x? A) 9 B) [#permalink]

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07 Mar 2008, 03:35
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
Senior Manager
Joined: 02 Dec 2007
Posts: 449

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07 Mar 2008, 06:41
Choice D

2^13( 2^2-1)= 3(2^13)
CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City

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07 Mar 2008, 07:11
japped187 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

d

factor out 2^x and move all variables to one side
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Manager
Joined: 21 Mar 2007
Posts: 73

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12 Mar 2008, 04:36
CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City

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12 Mar 2008, 04:49
see below
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_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

CEO
Joined: 29 Mar 2007
Posts: 2559

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12 Mar 2008, 07:37
japped187 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

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

2^x(1-1/4)=3(2^13) ---> 2^x(3/2^2)=3(2^13)

cancel the 3's. and multiply the 2^2

thus 2^x=2^15 or x=15

D
Manager
Joined: 05 Feb 2007
Posts: 140

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27 Mar 2008, 21:08
bmwhype...thanks for the full answer...but can anyone help me? I'm still confused on this one..
Director
Joined: 01 May 2007
Posts: 793

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28 Mar 2008, 07:57
You could just plug in the answer choices and solve until the right = left side.
Intern
Joined: 28 Mar 2008
Posts: 1

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28 Mar 2008, 20:36
japped187 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

since u need the LHS to come to 3(2^13), start substituting the values for x from the choices given.

first substitute 17 - it becomes 2^17-2^15 = 2^15(2^2 - 1) = 3. 2^15 - which is not what we want

so try the second bigger choice - 15

2^15-2^13 = 2^13( 2^2 - 1) = 3. 2^13 - which is what we want

hence , D is the choice
Director
Joined: 10 Sep 2007
Posts: 938

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28 Mar 2008, 20:42
A much shorter and direct way is following
2^x = 2^2 * 2^(x-2)
So expression in question should read
2^2 * 2^(x-2) - 2^(x-2) = 3(2^13)
2^(x-2)*3 = 3*2^13
=> x-2 = 13
=> x = 15

No need to put values or anything just plain straight forward.
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