If 2^x-2^(x-2)=3*2^13 what is the value of x?

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If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

02 Apr 2012, 14:05

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Question Stats:

83% (01:39) correct

16% (01:16) wrong

based on 2 sessions

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

[Reveal] Spoiler: OA

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Last edited by Bunuel on 02 Apr 2012, 18:04, edited 1 time in total.

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Re: Value of X [#permalink]

02 Apr 2012, 18:04

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enigma123 wrote:

If 2^x - 2^x ^ - ^2 = 3 (2^1^3) What is the value of x?

A) 9

B) 11

C) 13

D) 15

E) 17

Question should read;

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

2^x-2^{x-2}=3*2^{13} --> 2^x-2^{x}*2^{-2}=3*2^{13} --> 2^x-\frac{2^{x}}{2^{2}}=3*2^{13} --> 2^x(1-\frac{1}{2^{2}})=3*2^{13} --> 2^x*\frac{3}{2^{2}}=3*2^{13} --> 2^x=2^{15} --> x=15.

Answer: D.
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

03 Apr 2012, 07:09

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enigma123 wrote:

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

tricky....we would fall for 13...but answer is x-2=13 so x=15 i.e D
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Re: Value of X [#permalink]

05 Apr 2013, 00:50

Bunuel wrote:

2^x(1-\frac{1}{2^{2}})=3*2^{13} --> 2^x*\frac{3}{2^{2}}=3*2^{13}.

Bunuel, can you tell me what you did in these steps? Where does the 3 come from?

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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

05 Apr 2013, 02:45

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I can explain that:

2^x-2^x^-^2=2^x(1-2^-^2)=2^x(1-\frac{1}{2^2})=\frac{2^x*3}{4}=3*2^1^3
divide by 3
\frac{2^x}{4}=2^1^3=2^x^-^2=2^1^3

Hope now it's clear
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

05 Apr 2013, 06:06

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enigma123 wrote:

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

Just another way of doing this sum:
2^x-2^{x-2}= (4-1)*2^{13}

or 2^x-2^{x-2} = 2^{15}-2^{13}

Thus, x = 15.

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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

06 Apr 2013, 06:45

2^x - 2^(x-2) = {2^(x-2)} * ( 2^2 - 1) = {2^(x-2)} * 3 = 3 * 2^13
--> 2^(x-2) = 2^13
--> x-2 = 13
--> x = 15
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink] 06 Apr 2013, 06:45

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If 2^x-2^(x-2)=3*2^13 what is the value of x?

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