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# If 2^x - 2^(x-2) = 3(2^13), what is the value of x? 9 11 13

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Manager
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If 2^x - 2^(x-2) = 3(2^13), what is the value of x? 9 11 13 [#permalink]  27 May 2006, 08:12
If 2^x - 2^(x-2) = 3(2^13), what is the value of x?

9
11
13
15
17

Manager
Joined: 25 Apr 2006
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Ans: 15 [#permalink]  27 May 2006, 08:29
2^x-2^x/2^2

=>2^x(1-1/4)=>2^x(3/4) = 3 * 2^13
=>2^x = 3*2^13*(4/3) = 2^15
=>x=15
Manager
Joined: 13 Apr 2006
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How did you get 2^x(1-1/4)?
Sorry if that is a dumb question!
Manager
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2^x-2^x/2^2

taking 2^x common

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

Hope this is clear.
Director
Joined: 09 Oct 2005
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yessuresh wrote:
2^x-2^x/2^2

taking 2^x common

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

Hope this is clear.

2^x - 2^(x-2) = 3(2^13) what if we factore out 2^(x-2)?IMHO it is easier
2^(x-2){2^2-1}=3(2^13)
2^(x-2)*3=3(2^13)
2^(x-2)=2^13
x-2=13
x=15
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Director
Joined: 10 Oct 2005
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Since RHS is 3(2 raised 13) x can't be less than 13. Now plug in 15. Wow! this satisfies the equation
Manager
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Even dumber question...
What is LHS and RHS? I swear I took a prep course and we didn't
cover that!

BTW, it's nice outside. It's Memorial Day Weekend. Glad others can feel my anguish.
Senior Manager
Joined: 08 Jun 2004
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kuristar wrote:
Even dumber question...
What is LHS and RHS? I swear I took a prep course and we didn't
cover that!

LHS - left hand side
RHS - right hand side, please.
VP
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Yes it should be 15.
Manager
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x = 15

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

Factor out a 2^x on the left

yields

2^x(1-0.25) = 3(2^13)

2^x(3/4) = 3(2^13)

2^x.2^-2 = 2^13

x-2 =13

x=15
Manager
Joined: 04 May 2006
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x=15, same approach to take out a factor of 2^x from LHS and then resolve.
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