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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: 47157
If 4^x + 4^(-x) = 2, which of the following is the value of x?  [#permalink]

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20 Mar 2016, 23:30
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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

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Math Expert
Joined: 02 Aug 2009
Posts: 6258
Re: If 4^x + 4^(-x) = 2, which of the following is the value of x?  [#permalink]

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21 Mar 2016, 04:00
3
2
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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##### General Discussion
Intern
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, 22:12
2
1
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, 05:02
Thanks ! I love this method :
4^0+4^0=1+1=2 Ans. C
Intern
Joined: 10 Jul 2018
Posts: 5
could someone explain me step by step how to solve this kind of questi  [#permalink]

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12 Jul 2018, 09:28
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

could someone explain me step by step how to solve this kind of question? pls

it's easy, but the logic did't enter in my mind
Intern
Joined: 17 May 2018
Posts: 17
Re: could someone explain me step by step how to solve this kind of questi  [#permalink]

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12 Jul 2018, 09:43
Indeed, because we're not used to see x in the exponent and because there's not much we can do with the expression to reduce it with the exponent properties, let's try the answers.

You can quickly plug them and see that 0 is the one that works (remember that any number raised to 0 is 1).
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Joined: 14 Feb 2018
Posts: 380
Re: could someone explain me step by step how to solve this kind of questi  [#permalink]

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12 Jul 2018, 09:43
(4^2x + 1)/4^x = 2

Let 4^x = a
Thus, a^2 -2a +1 = 0.
a^2 - a - a + 1 = 0
a(a - 1) -1(a - 1) = 0.

Thus, a = 1 or 4^x = 1.

Clearly, x = 0.

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Re: could someone explain me step by step how to solve this kind of questi  [#permalink]

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12 Jul 2018, 10:06
joaolucas193 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

could someone explain me step by step how to solve this kind of question? pls

it's easy, but the logic did't enter in my mind

https://gmatclub.com/forum/if-4-x-4-x-2 ... 15347.html
Hi, kindly go through above link, especially the explanation by Chetan Sir.
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Re: could someone explain me step by step how to solve this kind of questi  [#permalink]

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12 Jul 2018, 10:17
joaolucas193 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

could someone explain me step by step how to solve this kind of question? pls

it's easy, but the logic did't enter in my mind

$$4^x + 4^{-x} = 2$$

Or, $$2^{2x} + 2^{-2x} = 2^1$$

Or, $$2^{2x} + \frac{1}{2^{2x}} = 2^1$$

Or, $$2^{4x} + 1 = 2$$

Or, $$2^{4x} = 1$$

Or, $$2^{4x} = 2^0$$

So, $$4x = 0$$

Or, x = 0, Answer must be (C) 0
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Abhishek....

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Posts: 37
Location: India
GMAT 1: 640 Q49 V27
GPA: 4
Re: If 4^x + 4^(-x) = 2, which of the following is the value of x?  [#permalink]

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12 Jul 2018, 11:34
joaolucas193 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

could someone explain me step by step how to solve this kind of question? pls

it's easy, but the logic did't enter in my mind

Yes. Only step is go by putting the values in options. When You put 0 you will get Your answer.
Intern
Joined: 11 Jul 2018
Posts: 16
Re: If 4^x + 4^(-x) = 2, which of the following is the value of x?  [#permalink]

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12 Jul 2018, 21:14
The approaches provided above are great and works really well if you are good with Maths.
For someone who would like to deal it in more easier manner.
Simply start putting values of X from options, also ensure first put integers and ignore fractions.

First option X = -1 will lead to 4^(-1) + 4^(-(-1)) = 4^(-1) + 4^1 = (1/4) + 4 = 4.25 So not an option.

Second integer option X = 0 (Note left option B as it was not integer and will make computation little tricky)
4^(0)+4^(-(0)) = 4^0+4^0 = 1 + 1 = 2

This method has deep flaw if all the options are integers.
All the more frustrating if first four options are integers and not the correct answer.
However, this may ring in well with few.
Re: If 4^x + 4^(-x) = 2, which of the following is the value of x? &nbs [#permalink] 12 Jul 2018, 21:14
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