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Got stuck on this one : If a is a perfect square, what is

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Got stuck on this one : If a is a perfect square, what is [#permalink] New post 10 Aug 2006, 22:21
Got stuck on this one :

If a is a perfect square, what is the value of a given :

a^x = 1/8 ;
x = 3/2 ( (log2(a)) - 3 ). ...........(2 is the base of log)

1) 1
2) 64
3) 4
4) 16
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 [#permalink] New post 10 Aug 2006, 22:23
I think log is outside the scope of GMAT.
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 [#permalink] New post 10 Aug 2006, 22:28
ps_dahiya wrote:
I think log is outside the scope of GMAT.


One of my friend gave it to me. Couldn't get it done so thought of asking.
I just started quant so not aware of the scope per se :oops: .
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 [#permalink] New post 12 Aug 2006, 09:20
buzzgaurav wrote:
ps_dahiya wrote:
I think log is outside the scope of GMAT.


One of my friend gave it to me. Couldn't get it done so thought of asking.
I just started quant so not aware of the scope per se :oops: .



NEVERTHELESS, lets try and solve this

Consider 1:

a^x = 1/8 = 2^(-3)
Since a is a perfect square ... a can be 4,9,16 etc. which gives different answers ... INSUFF

Consider 2:
Simplifying .. gives
a = (8) (2^(2x/3) ) , x is unknown therefore ... INSUFF

Consider 1 and 2:
simplifying using logs we get 2 equations:

from 1: x log a = -3
from 2: log a = 2x/3 +3

eliminating log a gives: 2x^2 + 9x + 9 = 0 or x = -3 and -3/2

solving for a gives a = 2 or a = 4

since a is a perfect square .. a = 4 ... SUFFICIENT.

Answer: C
  [#permalink] 12 Aug 2006, 09:20
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Got stuck on this one : If a is a perfect square, what is

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