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If 2^x - 2^x-2 = 3(2^13). What is x? a)9 b)11 c)13 d)15 e)17

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If 2^x - 2^x-2 = 3(2^13). What is x? a)9 b)11 c)13 d)15 e)17 [#permalink] New post 19 Oct 2006, 14:24
If 2^x - 2^x-2 = 3(2^13). What is x?

a)9

b)11

c)13

d)15

e)17
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 [#permalink] New post 19 Oct 2006, 15:08
15

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

2^x/2^2 = 2^13

x=15
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 [#permalink] New post 19 Oct 2006, 19:42
yes 15 as explained above.
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 [#permalink] New post 19 Oct 2006, 20:32
D

Simplify on the left:
2^x-2 ( 2^2 - 1)

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

x-2 = 13

x=15
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 [#permalink] New post 20 Oct 2006, 08:28
trivikram wrote:
15

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

2^x/2^2 = 2^13

x=15


How do you get to that part? I am having a problem simplifying the left side of the equation :cry:
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 [#permalink] New post 20 Oct 2006, 09:35
If 2^x - 2^x-2 = 3(2^13). What is x?

2^x(1 - 2^-2)=3(2^13)
2^x(3/4) = 3(2^13)
2^x/4 = 2^13
2^x = 2^15

x =15
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 [#permalink] New post 20 Oct 2006, 09:47
If 2^x - 2^x-2 = 3(2^13). What is x?

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

stem

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

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

2^x = 2^15

x = 15

My answe is D
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 [#permalink] New post 21 Oct 2006, 06:45
Matrix02 wrote:
trivikram wrote:
15

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

2^x/2^2 = 2^13

x=15


How do you get to that part? I am having a problem simplifying the left side of the equation :cry:


2^x - 2^x-2 is nothing but 2^x - 2^x/2^2

So take out 2^x common we get 2^x(1-1/2^2) = 2^x(1-1/4) = 2^x*3/4
  [#permalink] 21 Oct 2006, 06:45
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