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2^x - 2^x-2 = 3 (2^13), what is the value of x? a) 9 b)

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Intern
Joined: 15 Jul 2005
Posts: 25
2^x - 2^x-2 = 3 (2^13), what is the value of x? a) 9 b) [#permalink]

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01 Sep 2005, 06:08
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2^x - 2^x-2 = 3 (2^13), what is the value of x?

a) 9
b) 11
c) 13
d) 15
e) 17

Please explain the approach..thanks
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

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01 Sep 2005, 07:38
15...

here is how you do it...think factorization, think how can you make this look easy...so

factor 2^x-2 out on the LHS...

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

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

x-2=13

x=13+2=15...

remember think what can you factor out to make the equation look easy... you notice on the RHS of the equation you have a 3 (which is a prime) so your goal should be to some how factor the LHS such that you have a 3 somewhere....
Director
Joined: 15 Aug 2005
Posts: 796
Location: Singapore

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02 Sep 2005, 00:29
Fresinha12, Im sorry how did you get 2^(x-2)(2^2 - 1)=3(2^13)??
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Cheers, Rahul.

02 Sep 2005, 00:29
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2^x - 2^x-2 = 3 (2^13), what is the value of x? a) 9 b)

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