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Subtracting Exponents

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Intern
Intern
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Joined: 03 Feb 2009
Posts: 27

Kudos [?]: 22 [0], given: 0

Schools: Duke, UNC, Emory, Ga Tech, Vanderbilt, Indiana, Wash U, Texas, Rollins
Subtracting Exponents [#permalink]

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New post 03 Feb 2009, 15:27
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

Kudos [?]: 22 [0], given: 0

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CEO
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Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4590 [1], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User Premium Member
Re: Subtracting Exponents [#permalink]

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New post 03 Feb 2009, 15:34
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Expert's post
\(2^x - 2^{(x-2)} = 3*2^{13}\)

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

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

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

x-2=13

x=15
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Kudos [?]: 4590 [1], given: 360

Intern
Intern
avatar
Joined: 03 Feb 2009
Posts: 27

Kudos [?]: 22 [0], given: 0

Schools: Duke, UNC, Emory, Ga Tech, Vanderbilt, Indiana, Wash U, Texas, Rollins
Re: Subtracting Exponents [#permalink]

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New post 03 Feb 2009, 15:50
wow, well done. Thanks. I can't believe I missed that one. I guess the part where I got confused was factoring out the exponent (x-2). That makes sense though.

Kudos [?]: 22 [0], given: 0

Re: Subtracting Exponents   [#permalink] 03 Feb 2009, 15:50
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Subtracting Exponents

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