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# 2^x-2^(x-2)=3(2^13) what is the value of x? 9 11 13 15 17

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2^x-2^(x-2)=3(2^13) what is the value of x? 9 11 13 15 17 [#permalink]  12 Sep 2008, 15:39
2^x-2^(x-2)=3(2^13) what is the value of x?

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Re: gmat prep another exponent [#permalink]  12 Sep 2008, 15:49
X = 15 = D

2^x - 2^(x-2) = 3 * 2^13
(2^2 * 2^x) - 2^x / 2^2 = 3 * 2^13
(2^2 * 2^x) - 2^x = 3 * 2^13 * 2^2
2^x (2^2 -1 ) = 3 * 2^15
2^x (3) = 3 * 2^15
2^x = 2^15
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Re: gmat prep another exponent [#permalink]  12 Sep 2008, 16:14
asdert wrote:
X = 15 = D

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

how come 2^x is same as 2^2*2^x?
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Re: gmat prep another exponent [#permalink]  12 Sep 2008, 17:32
Since 2^(x-2) = 2^x / 2^2, I had to get the same numerator to the first part of the equation in order to subtract them.
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Re: gmat prep another exponent [#permalink]  12 Sep 2008, 19:34
For some reason, I got 11... What's the correct answer?
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Re: gmat prep another exponent [#permalink]  12 Sep 2008, 19:36
Youngd8 wrote:
2^x-2^(x-2)=3(2^13) what is the value of x?

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11
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17

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

--> 2^(x-2) *2^2- 2^(x-2)=3(2^13)
--> 2^(x-2) 3=3(2^13)
x=15
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Re: gmat prep another exponent   [#permalink] 12 Sep 2008, 19:36
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