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# Subtracting Exponents

Author Message
Intern
Joined: 03 Feb 2009
Posts: 27
Schools: Duke, UNC, Emory, Ga Tech, Vanderbilt, Indiana, Wash U, Texas, Rollins

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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
CEO
Joined: 17 Nov 2007
Posts: 3525
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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03 Feb 2009, 15:34
1
KUDOS
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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Intern
Joined: 03 Feb 2009
Posts: 27
Schools: Duke, UNC, Emory, Ga Tech, Vanderbilt, Indiana, Wash U, Texas, Rollins

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

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