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# If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?

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Director
Joined: 10 Feb 2006
Posts: 657
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2? [#permalink]

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23 Nov 2007, 08:56
2
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Difficulty:

55% (hard)

Question Stats:

69% (02:54) correct 31% (02:00) wrong based on 208 sessions

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If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?

A. 40
B. 20
C. 10
D. 5/2
E. 5/4

Solution :
[Reveal] Spoiler:
2^8x = 1600 (2^2x-2) ^2 = 2^4x-4
2^8x = 2^6 * 5 ^2

2^8x-6 = 5^2

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-4-4x-1600-what-is-the-value-of-4-x-161823.html
[Reveal] Spoiler: OA

_________________

GMAT the final frontie!!!.

SVP
Joined: 05 Jul 2006
Posts: 1747

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23 Nov 2007, 09:53
If 4 ^4x = 1600 ..........impossible
CEO
Joined: 17 Nov 2007
Posts: 3583
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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23 Nov 2007, 13:46
1
KUDOS
Expert's post
yezz wrote:
If 4 ^4x = 1600 ..........impossible

possible

4^(4*1,330482)=1600
Manager
Joined: 26 Sep 2007
Posts: 65

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23 Nov 2007, 14:11
2
KUDOS
If 4 ^4x = 1600 , what is the value of (4^x-1)^2 ?

40
20
10
5/2
5/4

solution :

2^8x = 1600 (2^2x-2) ^2 = 2^4x-4
2^8x = 2^6 * 5 ^2

2^8x-6 = 5^2

(4^x-1)^2 = 4^2x-2 = 4^2x/4^2 = 4^2x/16 ____________(1)

Now from 4^4x=1600, we can get a value of 4^2x
(4)^(2x)^2 = (40)^2
4^2x=40

Now plug in 4^2x value in eqn 1
40/16=5/2
VP
Joined: 08 Jun 2005
Posts: 1145

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23 Nov 2007, 14:15
sevenplus wrote:
If 4 ^4x = 1600 , what is the value of (4^x-1)^2 ?

40
20
10
5/2
5/4

solution :

2^8x = 1600 (2^2x-2) ^2 = 2^4x-4
2^8x = 2^6 * 5 ^2

2^8x-6 = 5^2

(4^x-1)^2 = 4^2x-2 = 4^2x/4^2 = 4^2x/16 ____________(1)

Now from 4^4x=1600, we can get a value of 4^2x
(4)^(2x)^2 = (40)^2
4^2x=40

Now plug in 4^2x value in eqn 1
40/16=5/2

4^(4*5/2) = 4^10 and not 1,600

Manager
Joined: 26 Sep 2007
Posts: 65

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23 Nov 2007, 14:56
KillerSquirrel wrote:
sevenplus wrote:
If 4 ^4x = 1600 , what is the value of (4^x-1)^2 ?

40
20
10
5/2
5/4

solution :

2^8x = 1600 (2^2x-2) ^2 = 2^4x-4
2^8x = 2^6 * 5 ^2

2^8x-6 = 5^2

(4^x-1)^2 = 4^2x-2 = 4^2x/4^2 = 4^2x/16 ____________(1)

Now from 4^4x=1600, we can get a value of 4^2x
(4)^(2x)^2 = (40)^2
4^2x=40

Now plug in 4^2x value in eqn 1
40/16=5/2

4^(4*5/2) = 4^10 and not 1,600

Question is asking to find out the value of (4^x-1)^2
So 5/2 is the value of (4^x-1)^2 and not of x
So you can't plug in x=5/2
Intern
Joined: 11 Nov 2007
Posts: 3

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23 Nov 2007, 18:36
sevenplus wrote:
If 4 ^4x = 1600 , what is the value of (4^x-1)^2 ?

40
20
10
5/2
5/4

solution :

2^8x = 1600 (2^2x-2) ^2 = 2^4x-4
2^8x = 2^6 * 5 ^2

2^8x-6 = 5^2

(4^x-1)^2 = 4^2x-2 = 4^2x/4^2 = 4^2x/16 ____________(1)

Now from 4^4x=1600, we can get a value of 4^2x
(4)^(2x)^2 = (40)^2
4^2x=40

Now plug in 4^2x value in eqn 1
40/16=5/2

Why (4^x - 1)^2 = 4^2x-2 ????

i thought (4^x - 1)^2 = 4^2x - 2 * 4^x + 1 ?
SVP
Joined: 29 Aug 2007
Posts: 2473

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23 Nov 2007, 21:54
sevenplus wrote:
KillerSquirrel wrote:
sevenplus wrote:
If 4 ^4x = 1600 , what is the value of (4^x-1)^2 ?

40
20
10
5/2
5/4

solution :

2^8x = 1600 (2^2x-2) ^2 = 2^4x-4
2^8x = 2^6 * 5 ^2

2^8x-6 = 5^2

(4^x-1)^2 = 4^2x-2 = 4^2x/4^2 = 4^2x/16 ____________(1)

Now from 4^4x=1600, we can get a value of 4^2x
(4)^(2x)^2 = (40)^2
4^2x=40

Now plug in 4^2x value in eqn 1
40/16=5/2

4^(4*5/2) = 4^10 and not 1,600

Question is asking to find out the value of (4^x-1)^2
So 5/2 is the value of (4^x-1)^2 and not of x
So you can't plug in x=5/2

why only 40 and not -40?

(4)^(2x)^2 = (40)^2
4^2x = +/- 40
Manager
Joined: 26 Sep 2007
Posts: 65

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24 Nov 2007, 15:01
GMAT TIGER wrote:
sevenplus wrote:
KillerSquirrel wrote:
sevenplus wrote:
If 4 ^4x = 1600 , what is the value of (4^x-1)^2 ?

40
20
10
5/2
5/4

solution :

2^8x = 1600 (2^2x-2) ^2 = 2^4x-4
2^8x = 2^6 * 5 ^2

2^8x-6 = 5^2

(4^x-1)^2 = 4^2x-2 = 4^2x/4^2 = 4^2x/16 ____________(1)

Now from 4^4x=1600, we can get a value of 4^2x
(4)^(2x)^2 = (40)^2
4^2x=40

Now plug in 4^2x value in eqn 1
40/16=5/2

4^(4*5/2) = 4^10 and not 1,600

Question is asking to find out the value of (4^x-1)^2
So 5/2 is the value of (4^x-1)^2 and not of x
So you can't plug in x=5/2

why only 40 and not -40?
(4)^(2x)^2 = (40)^2
4^2x = +/- 40

Because no answer choice is -ve
SVP
Joined: 05 Jul 2006
Posts: 1747

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24 Nov 2007, 22:33
walker wrote:
yezz wrote:
If 4 ^4x = 1600 ..........impossible

possible

4^(4*1,330482)=1600

walker still dont get it??

4^y is a repitition of the factors 2 multiplied by each other

to get 1600 ( we need a 5 factor ) ... what am i doing wrong here??
CEO
Joined: 17 Nov 2007
Posts: 3583
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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24 Nov 2007, 23:43
Maybe (4^x-1)^2 means (4^(x-1))^2

otherwise
((4^x)-1)^2~28

yezz wrote:
walker wrote:
yezz wrote:
If 4 ^4x = 1600 ..........impossible

possible

4^(4*1,330482)=1600

walker still dont get it??

4^y is a repitition of the factors 2 multiplied by each other

to get 1600 ( we need a 5 factor ) ... what am i doing wrong here??

you are right in the case of x-integer. But finding x from 4^(4*x)=1600 is out of scope of GMAT. (I use MS Excel to calculate x)
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15908
Re: If 4 ^4x = 1600 , what is the value of (4^x-1)^2 ? 40 20 10 [#permalink]

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14 Dec 2013, 13:18
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Posts: 39575
Re: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2? [#permalink]

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15 Dec 2013, 04:32
4
KUDOS
Expert's post
If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
A. 40
B. 20
C. 10
D. 5/2
E. 5/4

$$4^{4x} = 1600$$ --> $$4^{2x} = 40$$ -

$$4^{(x-1)^2}=4^{2(x-1)}=4^{2x-2}=\frac{4^{2x}}{4^2}=\frac{40}{16}=\frac{5}{2}$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-4-4x-1600-what-is-the-value-of-4-x-161823.html[/quote]
_________________
Re: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?   [#permalink] 15 Dec 2013, 04:32
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