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by Anurag@Gurome » Mon Nov 07, 2011 10:18 pm
gmatblood wrote:If (4)^(4x) = 1600, what is the value of (4^[x-1])^2?
--> 4^(4x) = 1600
--> (4^x)^4 = 1600
--> (4^x)^2 = 40

Now, 4^(x-1) = [(4^x)/4]

Hence, (4^[x-1])^2 = [(4^x)/4]^2 = (4^x)^2/(4^2) = 40/16 = 5/2

The correct answer is D.
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by neelgandham » Wed Nov 09, 2011 1:41 am
If (4)^(4x) = 1600, what is the value of (4^[x-1])^2?, The question can be rephrased to 'What is the value of (4^2x)/(4^2)?'.

Solving for 4^2x.
(4)^(4x) = 1600
(4^2x)^2 = 1600
4^2x = Square root (1600) = 40 (Not -40 because the term square root (1600) is equal to square of a number (4^x), hence it is always positive)

value of (4^2x)/(4^2) = 40/16 = 5/2

D
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