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Manhattan GMAT Question
Source: Beat The GMAT — Problem Solving |
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
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
(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
= (4)^2x-2
= ((4)^2x)/(4)^2
= ((4)^2x)/16
=(4)^(4x/2)/16
=[(1600)^(1/2)]/16
=40/16
=5/2
(4^x)^4 =20^4gabriel16 wrote:If 4^4x = 1600, what is the value of (4^x–1)^2?
Any help is greatly appreciated. Thanks.
4^x=20
(4^(x-1))^2 = (4^x/4)^2= (20/4)^2 = 25/4
Great stuff. I ran across this question on a MGMAT practice test and couldn't figure it out at first. Thanks for your help.
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
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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sureshbala
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Folks, this was answered earlier....Here is the link
https://www.beatthegmat.com/exponents-pr ... tml#123429
https://www.beatthegmat.com/exponents-pr ... tml#123429
