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2^ (2 x - 1) = 8^y

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by sanju09 » Fri Mar 04, 2011 12:55 am
If 2^ (2 x - 1) = 8^y then x in terms of y equals:
(A) 2 y - l
(B) ½ (3 y + 1)
(C) ½ (y - l)
(D) ½ (y + l)
(E) ½ (3 y - 1)
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by BarryLi » Fri Mar 04, 2011 1:02 am
2^(2x-1) = 8^y
2^(2x-1) = (2^y)(2^y)(2^y)
2^(2x-1) = 2^(3y)
2x-1 = 3y
2x = 3y+1
x = (3y+1) / 2

OA: B, although the character for 1/2 doesn't display correctly on my computer.
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by Night reader » Fri Mar 04, 2011 6:52 am
2^ (2 x - 1) = 2^3y
2x-1=3y, x=(3y+1)/2

answer B
sanju09 wrote:If 2^ (2 x - 1) = 8^y then x in terms of y equals:
(A) 2 y - l
(B) ½ (3 y + 1)
(C) ½ (y - l)
(D) ½ (y + l)
(E) ½ (3 y - 1)
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by GMATGuruNY » Fri Mar 04, 2011 7:38 am
sanju09 wrote:If 2^ (2 x - 1) = 8^y then x in terms of y equals:
(A) 2 y - l
(B) ½ (3 y + 1)
(C) ½ (y - l)
(D) ½ (y + l)
(E) ½ (3 y - 1)
Plug in x = 2.
2^(2*2 - 1) = 8^y.
2^3 = 8^y.
8 = 8^y.
y = 1.

Now we plug y=1 into all the answers to see which yields our target of 2 (the value of x).

Only answer choice B works:
1/2(3*1 + 1) = 1/2*4 = 2.

The correct answer is B.
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