Exponent Question: Please Help.

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blemming: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Tue Nov 03, 2009 9:23 pm

by blemming » Fri Feb 12, 2010 8:17 am

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

I cannot figure this problem out for the life of me. Again, I see the right answer, but I do not understand how they arrive at it without actually taking 2^13 and multiplying it by 3.

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Source: Beat The GMAT — Problem Solving | Fri Feb 12, 2010 8:17 am

junis1: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Wed Jan 13, 2010 11:07 am; Thanked: 1 times

by junis1 » Fri Feb 12, 2010 9:16 am

IMO [assuming 2^x-2 = 2^(x-2)]:

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

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

2^x (1 - 1/4) = 3(2^13)

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

2^x [ 3/(2^2) ] = 3(2^13)

3 [(2^x) / (2^2)] = 3(2^13)

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

x-2 = 13 => x=15

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sars72: Master | Next Rank: 500 Posts; Posts: 241; Joined: Wed Jan 27, 2010 10:10 pmFollowed by: 2 members; Location: Chennai; Thanked: 23 times; GMAT Score:690

by sars72 » Fri Feb 12, 2010 10:47 am

wow! awesome, junis1.. and your first post at that.

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Fri Feb 12, 2010 10:51 am

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

I cannot figure this problem out for the life of me. Again, I see the right answer, but I do not understand how they arrive at it without actually taking 2^13 and multiplying it by 3.

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