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Exponent Question: Please Help.

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Junior | Next Rank: 30 Posts
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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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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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by sars72 » Fri Feb 12, 2010 10:47 am
wow! awesome, junis1.. and your first post at that.
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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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