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

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If 4^(4x) = 1600, what is the value of [4^(x–1)]^2? [#permalink] New post 23 Nov 2007, 07:56
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Question Stats:

65% (02:55) correct 35% (02:02) wrong based on 113 sessions
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

We can't have a value of x that would = 5 ^2. Please help.


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

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 [#permalink] New post 23 Nov 2007, 08:53
If 4 ^4x = 1600 ..........impossible
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 [#permalink] New post 23 Nov 2007, 12:46
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Expert's post
yezz wrote:
If 4 ^4x = 1600 ..........impossible

possible

4^(4*1,330482)=1600
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Re: Number - MGMT [#permalink] New post 23 Nov 2007, 13:11
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alimad 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

We can't have a value of x that would = 5 ^2. Please help.


Answer is D. 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
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Re: Number - MGMT [#permalink] New post 23 Nov 2007, 13:15
sevenplus wrote:
alimad 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

We can't have a value of x that would = 5 ^2. Please help.


Answer is D. 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

:)
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Re: Number - MGMT [#permalink] New post 23 Nov 2007, 13:56
KillerSquirrel wrote:
sevenplus wrote:
alimad 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

We can't have a value of x that would = 5 ^2. Please help.


Answer is D. 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
:)
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Re: Number - MGMT [#permalink] New post 23 Nov 2007, 17:36
sevenplus wrote:
alimad 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

We can't have a value of x that would = 5 ^2. Please help.


Answer is D. 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 ?
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Re: Number - MGMT [#permalink] New post 23 Nov 2007, 20:54
sevenplus wrote:
KillerSquirrel wrote:
sevenplus wrote:
alimad 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

We can't have a value of x that would = 5 ^2. Please help.


Answer is D. 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
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Re: Number - MGMT [#permalink] New post 24 Nov 2007, 14:01
GMAT TIGER wrote:
sevenplus wrote:
KillerSquirrel wrote:
sevenplus wrote:
alimad 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

We can't have a value of x that would = 5 ^2. Please help.


Answer is D. 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 :)
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 [#permalink] New post 24 Nov 2007, 21:33
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??
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 [#permalink] New post 24 Nov 2007, 22:43
Expert's post
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)
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Re: If 4 ^4x = 1600 , what is the value of (4^x-1)^2 ? 40 20 10 [#permalink] New post 14 Dec 2013, 12:18
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Re: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2? [#permalink] New post 15 Dec 2013, 03:32
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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

\(4^{4x} = 1600\) --> \(4^{2x} = 40\) -

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

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-4-4x-1600-what-is-the-value-of-4-x-161823.html[/quote]
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Re: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?   [#permalink] 15 Dec 2013, 03:32
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