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

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Question Stats:

58% (02:29) correct

42% (01:58) wrong

based on 75 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 :

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
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If 4 ^4x = 1600 ..........impossible

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yezz wrote:

If 4 ^4x = 1600 ..........impossible

possible

4^(4*1,330482)=1600

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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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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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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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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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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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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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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

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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 ]
14 Dec 2013, 12:18

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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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Re: If 4^(4x) = 1600, what is the value of [4^(x–1)]^2?
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15 Dec 2013, 03:32