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Value of X - Exponents

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Junior | Next Rank: 30 Posts
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by adi » Sat Mar 08, 2008 2:31 pm
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

The answer should be D.
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Source: — Problem Solving |
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Re: Value of X - Exponents

by netigen » Sat Mar 08, 2008 3:16 pm
adi wrote: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

The answer should be D.
Equate the equation
(2^x) - (2^[x-2]) = (2^x) [1 - (2^[-2])] = (2^x) [1 - 1/4] = 3/4 x 2^x

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

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

x-2 = 13

x= 15
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Junior | Next Rank: 30 Posts
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by adi » Sat Mar 08, 2008 3:50 pm
How did you make (2^x) - (2^[x-2]) = (2^x) [1 - (2^[-2])]

Also, where did the - go in (2^x) - (2^[x-2])
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by tony777 » Sun Mar 09, 2008 4:47 am
(2^x) - (2^[x-2]) = (2^x) [1 - (2^[-2])]

In netigen's response he/she factored (2^x) - (2^[x-2]) to bring 2^x out.
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Shortest Way to Solve

by opengmat » Fri Mar 14, 2008 11:45 pm
The shortest to solve is by plug-in answer choice and equate both sides.

here start with C > LHS < RHS [x=13]
Goto next choice D > LHS = RHS [x=15]

Pls comment,
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backsolving

by resilient » Tue Mar 18, 2008 12:03 am
this is a fairly involved question. I would definintely try to backsolve on this question. It is begging to be back solved. In fact, I dont even see how to equate the equation.
Appetite for 700 and I scraped my plate!
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by xilef » Tue Mar 18, 2008 12:44 pm
once you realize that (2^x-2) is 2^x/2^2 then:

2^x-(2^x/2^2)=3(2^13)
2^x(1-1/4)=3(2^13)
2^x(3/4)=3(2^13)
2^x=4(2^13)
2^x=2^2(2^13)
2^x=(2^15)
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by hillzheng » Wed Apr 16, 2008 10:29 pm
yes, x=15 or answer be D
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by aj5105 » Thu May 07, 2009 10:39 pm
Stuart's reply : https://www.beatthegmat.com/exponent-pro ... 17726.html
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by pacogzza » Mon Aug 23, 2010 5:33 pm
Sorry guys, I did not get the process of how you guys went through this problem... Could you go over this prob again and explain it for dummies plz??

Saludos from Mexico (regards from Mexico)
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