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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]

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29 Jan 2006, 13:02
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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
VP
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29 Jan 2006, 14:21
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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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

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29 Jan 2006, 15:13
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
Manager
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29 Jan 2006, 17:51
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, 07:38, edited 1 time in total.
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29 Jan 2006, 20:19
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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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

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30 Jan 2006, 07:45
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!
Manager
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30 Jan 2006, 08:13
I like this problem. Would this be considered intermediate or difficult in the actual test?

Thanks.
Senior Manager
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30 Jan 2006, 15:11
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
30 Jan 2006, 15:11
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