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If 2^x - 2^(x-2) = 3(2^13), what is the value of x? A. 9

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If 2^x - 2^(x-2) = 3(2^13), what is the value of x? A. 9  [#permalink] New post 29 Jan 2006, 12:02
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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
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 [#permalink] New post 29 Jan 2006, 13:21
Is it 15?

2^x-2^(x-2) = 2^(x-2) [2^2 - 1] = 2^(x-2) * 3

So 2^(x-2) * 3 = 3 * 2^13
which gives
x-2 = 13
or x = 15.
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 [#permalink] New post 29 Jan 2006, 14:13
2^x - 2^(x-2) = 3(2^13)

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

2^x * 2^-2 = 2^13

x-2 = 13

x=15
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 [#permalink] New post 29 Jan 2006, 16:51
allabout-
can you explain how
2^x * ( 1- 2^-2) = 3(2^13)
reduces to:
2^x * 2^-2 = 2^13

or giddi77, can you explain how

2^x-2^(x-2)
reduces to
2^(x-2) [2^2 - 1]
and then
2^(x-2) * 3

Last edited by kook44 on 30 Jan 2006, 06:38, edited 1 time in total.
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 [#permalink] New post 29 Jan 2006, 19:19
kook44 wrote:
giddi77, can you explain how

2^x-2^(x-2)
reduces to
2^(x-2) [2^2 - 1]
and then
2^(x-2) * 3


OK 2^x can be written as 2^(x+2-2) = 2^(x-2) * 2^2.

Hence 2^x - 2^(x-2) = 2^(x-2)* 2^2 - 2^(x-2) = 2^(x-2) [ 2^2 -1] by taking out the common factor 2^(x-2)

HTH.
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 [#permalink] New post 30 Jan 2006, 06:45
Quote:
OK 2^x can be written as 2^(x+2-2) = 2^(x-2) * 2^2.


argh. very clever!
That was what i was missing.
Guess I really have to train my brain to start thinking that way.

Thanks!
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 [#permalink] New post 30 Jan 2006, 07:13
I like this problem. Would this be considered intermediate or difficult in the actual test?

Thanks.
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 [#permalink] New post 30 Jan 2006, 14:11
yes my answer is also D.

2^x - 2^(x-2) = 3 * 2^13
=>2^x - 2^x/2^2 = 3 * 2^13
=> (2^2 . 2^x - 2^x)/2^2= 3 * 2^13
=> 3*2^x == 3 * 2^15
therefore x = 15
  [#permalink] 30 Jan 2006, 14:11
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If 2^x - 2^(x-2) = 3(2^13), what is the value of x? A. 9

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