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4^x + 4 ^-x = 2 What is the value of X

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Joined: 18 Jan 2012
Posts: 21
4^x + 4 ^-x = 2 What is the value of X  [#permalink]

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Updated on: 25 Jan 2014, 08:57
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6
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Difficulty:

5% (low)

Question Stats:

81% (01:18) correct 19% (01:48) wrong based on 429 sessions

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4^x + 4^-x = 2 What is the value of x?

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

Originally posted by nimc2012 on 07 Feb 2012, 08:56.
Last edited by Bunuel on 25 Jan 2014, 08:57, edited 2 times in total.
Edited the question
Math Expert
Joined: 02 Sep 2009
Posts: 51258
4^x + 4 ^-x = 2 What is the value of X  [#permalink]

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21 Mar 2016, 03:00
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

Plug-in method should work form most of the people.

Else you can realize that $$4^x+\frac{1}{4^x}=2$$ is the sum of a positive number and its reciprocal and it to equal to 2 each must be 1 --> $$4^x=\frac{1}{4^x}=1$$ --> $$x=0$$;

Or: let $$4^x=a$$ --> $$a+\frac{1}{a}=2$$ --> $$\frac{a^2+1}{a}=2$$ --> $$a^2−2a+1=0$$ --> $$(a−1)^2=0$$ --> $$a=1$$ --> $$4^x=a=1$$ --> $$x=0$$.

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Re: 4^x + 4 ^-x = 2 What is the value of X  [#permalink]

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25 Jun 2013, 04:56
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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Re: 4^x + 4 ^-x = 2 What is the value of X  [#permalink]

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25 Jun 2013, 11:41
3
4^x + 4^-x = 2 What is the value of x?

a) -1
b) -1/2
c) 0
d) 1/2
e) 1

Both X and -X are present in the equation as exponents. Hence if there is any solution to the equation, there would be another solution to the equation with the same absolute value and opposite polarity and so there cannot be a unique solution. So hypothetically if -1 is the answer then +1 would also be a solution and the same for -1/2 and +1/2. '0' is the only number without polarity. Hence answer is C
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Re: 4^x + 4 ^-x = 2 What is the value of X  [#permalink]

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13 Aug 2013, 19:38
Can someone please let me know if this method is a correct way to solve this problem?

My work:
4^x+4^-x=2
2^2x+2^-2x=2^1
2^2x (1+1)=2^1
2^2x(2^1)=2^1
(Same bases, so remove them)
2x+1=1
x=0

Please let me know if you can or CANNOT do this! Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 51258
Re: 4^x + 4 ^-x = 2 What is the value of X  [#permalink]

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14 Aug 2013, 00:03
1
onsameline wrote:
Can someone please let me know if this method is a correct way to solve this problem?

My work:
4^x+4^-x=2
2^2x+2^-2x=2^1
2^2x (1+1)=2^1
2^2x(2^1)=2^1
(Same bases, so remove them)
2x+1=1
x=0

Please let me know if you can or CANNOT do this! Thanks!

The red part is not correct:

$$2^{2x}+2^{-2x}=2^1$$ --> $$2^{2x}+\frac{1}{2^{2x}}=2^1$$ --> you cannot factor out 2^2x from LHS the way you did.

Hope it's clear.
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Re: 4^x + 4 ^-x = 2 What is the value of X  [#permalink]

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25 Feb 2014, 22:12
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

Alternate Solution:

4^x + 4 ^-x = 2

Can be written as

(2^x) ^ 2 - 2 + 1/(2^x) ^ 2 = 0

(2^x - 1/2^x ) ^ 2 = 0 (The above LHS equation is a perfect square)

2^x = 1/2^x = 2^-x

So x = -x = 0 Answer = C
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Re: 4^x + 4 ^-x = 2 What is the value of X  [#permalink]

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25 Feb 2014, 22:55
nimc2012 wrote:
4^x + 4^-x = 2 What is the value of x?

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

If we plug from the answer options we get x = 0 as 4^0 + 4^0 = 2
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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, 09:17
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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Re: If 4^x + 4^(-x) = 2, which of the following is the value of x?  [#permalink]

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12 Jul 2018, 10:34
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.
Re: If 4^x + 4^(-x) = 2, which of the following is the value of x? &nbs [#permalink] 12 Jul 2018, 10:34
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