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

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

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New post 11 May 2016, 05:15
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (01:01) correct 19% (01:21) wrong based on 152 sessions

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Posts: 1868
Re: If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =  [#permalink]

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New post 11 May 2016, 05:22
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
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V
Joined: 02 Aug 2009
Posts: 8343
If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =  [#permalink]

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New post 11 May 2016, 05:28
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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Re: If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =  [#permalink]

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New post 11 May 2016, 06:46
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.
Hence answer is 'E'
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Re: If y ¤ x = y^(2x) for all positive integers, then (3 ¤ 4) ¤ 2 =   [#permalink] 11 May 2016, 06:46
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