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Manhattan GMAT Question

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by gabriel16 » Wed Feb 11, 2009 5:36 am
If 4^4x = 1600, what is the value of (4^x–1)^2?


Any help is greatly appreciated. Thanks.
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by DanaJ » Wed Feb 11, 2009 6:02 am
4^4x means 4 raised to the 4x-th power, which cannot be 1600. Doing the prime factorization of 1600 you get that it is equal to (4^3)*(5^2), so it cannot be a power of 4. Therefore IMHO your equation is not correctly written.
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by jail » Wed Feb 11, 2009 8:23 am
This can be solved:

4^4x = 2^8x and 1600 = 40^2 = (5^2)*(2^6) , therefore

2^8x=(5^2)*(2^6) Multiply both with the power 1/2

2^4x= 5 * 2^3 Thus 2^4x = 40 ---> a

Now we are looking for (4^x–1)^2 which is = 2^4x-4

2^4x-4 = 2^4x * 1/16 Now sustitute with a

40 * 1/16 = 5/2
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by sastagi » Wed Feb 11, 2009 9:56 am
(4^x-1)^2

= (4)^2x-2

= ((4)^2x)/(4)^2

= ((4)^2x)/16

=(4)^(4x/2)/16

=[(1600)^(1/2)]/16

=40/16

=5/2
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Re: Manhattan GMAT Question

by x2suresh » Wed Feb 11, 2009 10:11 am
gabriel16 wrote:If 4^4x = 1600, what is the value of (4^x–1)^2?


Any help is greatly appreciated. Thanks.
(4^x)^4 =20^4

4^x=20


(4^(x-1))^2 = (4^x/4)^2= (20/4)^2 = 25/4
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by gabriel16 » Wed Feb 11, 2009 10:36 am
Great stuff. I ran across this question on a MGMAT practice test and couldn't figure it out at first. Thanks for your help.
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by sacx » Thu Feb 12, 2009 2:27 am
If 4^4x = 1600, what is the value of (4^x–1)^2

4^4x => 4^2x * 4^2x
1600 = > 40 * 40

(4^x–1)^2 = (4^2x)/ 16

= 40/16 => 5/2
SACX
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by sureshbala » Thu Feb 12, 2009 2:36 am
Folks, this was answered earlier....Here is the link

https://www.beatthegmat.com/exponents-pr ... tml#123429
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