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# If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =

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Math Expert
Joined: 02 Sep 2009
Posts: 62690
If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =  [#permalink]

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11 May 2016, 04:15
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82% (01:00) correct 18% (01:21) wrong based on 153 sessions

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If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =

A. 3^8
B. 3^12
C. 3^16
D. 3^24
E. 3^32

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Joined: 06 Nov 2014
Posts: 1864
Re: If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =  [#permalink]

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11 May 2016, 04:22
Bunuel wrote:
If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =

A. 3^8
B. 3^12
C. 3^16
D. 3^24
E. 3^32

y ¤ x = y^(2x)
3 ¤ 4 = 3^(8)

(3 ¤ 4) ¤ 2 = (3^8) ¤ 2 = (3^8)^4 = 3^32

Correct Option: E
Math Expert
Joined: 02 Aug 2009
Posts: 8334
If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =  [#permalink]

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11 May 2016, 04:28
Bunuel wrote:
If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =

A. 3^8
B. 3^12
C. 3^16
D. 3^24
E. 3^32

Hi,

$$(3 ¤ 4) ¤ 2 = (3^{2*4})^{2*2} = (3^8)^4 = 3^{8*4}= 3^32$$

The portion where someone can make an error..
$$(3^8)^4 \neq {3^{8+4}}$$
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Joined: 18 Oct 2014
Posts: 778
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =  [#permalink]

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11 May 2016, 05:46
Bunuel wrote:
If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =

A. 3^8
B. 3^12
C. 3^16
D. 3^24
E. 3^32

(3^8)^4= 3^32.
_________________
I welcome critical analysis of my post!! That will help me reach 700+
Re: If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =   [#permalink] 11 May 2016, 05:46
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