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If 4^4x = 1600, what is the value of (4^(x 1))^2? 40 20 10

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Senior Manager
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Joined: 05 Oct 2008
Posts: 258
If 4^4x = 1600, what is the value of (4^(x 1))^2? 40 20 10 [#permalink]

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New post Updated on: 11 Dec 2008, 09:02
If 4^4x = 1600, what is the value of (4^(x–1))^2?

40
20
10
5/2
5/4

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Originally posted by study on 11 Dec 2008, 02:45.
Last edited by study on 11 Dec 2008, 09:02, edited 1 time in total.
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Re: Exponents [#permalink]

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New post 11 Dec 2008, 03:13
Please post the question correctly. I guess the qs is

4^(x-1)^2 i.e 4^(2x-2)
In which case the answer should be D

4^4x = 1600
take root of both sides
4^2x = 40

Substitute the value in the qs

4^2x / 4^2
40/16 = 5/2

If its the way you have printed the qs (4^x - 1 )^2
then 4^x = sqrt(40)

hence (4^x - 1 )^2 =
4^(2x) - 2*4^(x) + 1
40 - 2* sqrt(40) + 1
41 - 2* sqrt(40)
The value is between 27 and 29 , it cannot be evaluated into any given answers .
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Re: Exponents [#permalink]

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New post 11 Dec 2008, 09:04
i just copy pasted the problem from the source.
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Re: Exponents [#permalink]

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New post 12 Dec 2008, 12:58
I would go with D - 5/2 . Here is my explanation.

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

Above equation is same = 4 ^ (2x-2) ==> 4 ^2x / 4 ^2 -----Eq 1

Given 4 ^ 4x = 1600 ==> (4 ^2x) ^2 = 1600 ---> Eq 2

Take the SQRT on both sides in Eq 2
==> 4 ^ 2x = 40

Replacing 4 ^2 in eq 1, we get 40 / 4 ^ 2 ==> 40 / 26 ==> 5/2

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: Exponents   [#permalink] 12 Dec 2008, 12:58
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If 4^4x = 1600, what is the value of (4^(x 1))^2? 40 20 10

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