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

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Math Expert
Joined: 02 Sep 2009
Posts: 43831
If 4^x + 4^(-x) = 2, which of the following is the value of x? [#permalink]

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20 Mar 2016, 22:30
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Question Stats:

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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
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Aug 2009
Posts: 5658
Re: If 4^x + 4^(-x) = 2, which of the following is the value of x? [#permalink]

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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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Joined: 13 Sep 2015
Posts: 7
Re: If 4^x + 4^(-x) = 2, which of the following is the value of x? [#permalink]

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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
Intern
Joined: 29 Jun 2016
Posts: 1
Re: If 4^x + 4^(-x) = 2, which of the following is the value of x? [#permalink]

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15 Jul 2016, 04:02
Thanks ! I love this method :
4^0+4^0=1+1=2 Ans. C
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Posts: 13817
Re: If 4^x + 4^(-x) = 2, which of the following is the value of x? [#permalink]

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

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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