Exponents, find value of X

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rerika01: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Tue Aug 31, 2010 7:40 am; Thanked: 2 times

by rerika01 » Mon Jul 04, 2011 7:02 pm

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

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

The answer is 15. I just don't know how to get to 15.

thanks!

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Source: Beat The GMAT — Problem Solving | Mon Jul 04, 2011 7:02 pm

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Mon Jul 04, 2011 7:08 pm

Hi,
2^x = 2^(x-2+2) = 2^2*2^(x-2) = 4.2^(x-2)
So, 2^x - 2^x-2 = 4*2^(x-2) - 2^(x-2) = 3*2^(x-2) = 3*2^13
So, x-2 = 13 => x=15

Hence, D

Cheers!

Things are not what they appear to be... nor are they otherwise

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sunilrawat: Master | Next Rank: 500 Posts; Posts: 112; Joined: Sun Jun 13, 2010 9:20 am; Thanked: 5 times; GMAT Score:640

by sunilrawat » Mon Jul 04, 2011 8:58 pm

rerika01 wrote:2^x - 2^x-2 = 3(2^13), what is the value of x?

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

The answer is 15. I just don't know how to get to 15.

thanks!

2^x - 2^x-2 = 3(2^13)
2^x(1 - 2^-2) = 3(2^13)
3*2^(x-2) = 3(2^13)
x-2 = 13,
x = 15

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