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If 4^x + 4^(-x) = 2, which of the following is the value of x?

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If 4^x + 4^(-x) = 2, which of the following is the value of x? [#permalink]

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New post 20 Mar 2016, 22:30
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A
B
C
D
E

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Question Stats:

79% (01:10) correct 21% (01:26) wrong based on 177 sessions

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Re: If 4^x + 4^(-x) = 2, which of the following is the value of x? [#permalink]

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New post 21 Mar 2016, 03:00
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Bunuel wrote:
If 4^x + 4^(-x) = 2, which of the following is the value of x?

A. -1
B. -1/2
C. 0
D. 1/2
E. 1


Hi,

the first thing that one should get in mind is RHS is 2 and LHS has two terms with power of x..
power to 0 will make each of the two terms 1 and thus total will be two..
ans 0..

otherwise
\(4^x + 4^{-x} = 2\)
\(4^x + \frac{1}{4^x}= 2\)
let 4^x=a..
\(a + \frac{1}{a}= 2\)..
\(\frac{{a^2+1-2a}}{a}=0\)..
so \(\frac{{(a-1)^2}}{a}=0\)..

so\(a=1 or 4^x=1\)
so x=0
ans C

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Re: If 4^x + 4^(-x) = 2, which of the following is the value of x? [#permalink]

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New post 21 Mar 2016, 21:12
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If 4^x + 4^(-x) = 2, which of the following is the value of x?

A. -1
B. -1/2
C. 0
D. 1/2
E. 1

Plugging in Method:

4^0+4^0=1+1=2 Ans. C
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Re: If 4^x + 4^(-x) = 2, which of the following is the value of x? [#permalink]

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New post 15 Jul 2016, 04:02
Thanks ! I love this method :
4^0+4^0=1+1=2 Ans. C
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Re: If 4^x + 4^(-x) = 2, which of the following is the value of x? [#permalink]

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New post 06 Aug 2017, 11:20
Hello from the GMAT Club BumpBot!

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Re: If 4^x + 4^(-x) = 2, which of the following is the value of x?   [#permalink] 06 Aug 2017, 11:20
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