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

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

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07 Feb 2012, 09:56
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Jan 2014, 09:57, edited 2 times in total.
Edited the question
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Re: 4^x + 4 ^-x = 2 What is the value of X [#permalink]

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07 Feb 2012, 10:22
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

Thanks

0 (you can try and plug)
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Re: 4^x + 4 ^-x = 2 What is the value of X [#permalink]

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07 Feb 2012, 10:50
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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

Thanks

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 --> $$4^x=1$$ --> $$x=0$$;

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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07 Feb 2012, 12:41
thank you so much...it was an easy question!
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Re: 4^x + 4 ^-x = 2 What is the value of X [#permalink]

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07 Feb 2012, 14:48
That's easy and thanks for the explanation
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Re: 4^x + 4 ^-x = 2 What is the value of X [#permalink]

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25 Jun 2013, 05:56
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

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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, 07:35
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

Thanks

X^0 = 1 for all values of X

4^0 + 4^-1/2 --> 4^0 + 1/4^0 --> 1 + 1 = 2
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Re: 4^x + 4 ^-x = 2 What is the value of X [#permalink]

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25 Jun 2013, 12:41
3
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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

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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25 Jun 2013, 17:45
1
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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

let 4^x = t

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

t-1=0
t=1
4^x=1

x=0

Ans: 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, 20:38
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!
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Re: 4^x + 4 ^-x = 2 What is the value of X [#permalink]

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14 Aug 2013, 01:03
1
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Expert's post
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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14 Aug 2013, 14:39
Bunuel wrote:
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.

Thank you! So, is there pretty much no way to factor this $$2^{2x}+2^{-2x}=2^1$$
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Re: 4^x + 4 ^-x = 2 What is the value of X [#permalink]

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15 Aug 2013, 04:45
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!

2^2x+2^-2x=2^1
or, 2^2x (1+2^-4x)=2^1

No 1 there..............
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Re: 4^x + 4 ^-x = 2 What is the value of X [#permalink]

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25 Jan 2014, 09:51
Or one can also remember the following property

2^x + 2^x = 2^x+1

Here x+1 = 1, so x=0

In stem we have

2^2x + 2^-2x= 1

We can replace x = 0 and see that equation holds

Thus C is the correct answer
If this helps press Kudos!

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

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25 Feb 2014, 23:12
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, 23:55
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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4^x + 4 ^-x = 2 What is the value of X [#permalink]

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08 Mar 2015, 05:38
I can actually see that the only logical reason is if x = 0.

But why does the equation fail here: 2^2x + 2^-2x = 2^1

Shouldnt it, accordingly be 2x - 2x = 1?
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Re: 4^x + 4 ^-x = 2 What is the value of X [#permalink]

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08 Mar 2015, 06:51
Expert's post
erikvm wrote:
I can actually see that the only logical reason is if x = 0.

But why does the equation fail here: 2^2x + 2^-2x = 2^1

Shouldnt it, accordingly be 2x - 2x = 1?

It does not work that way at all. Check links here: 4-x-4-x-2-what-is-the-value-of-x-127194.html#p1239438
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Re: 4^x + 4 ^-x = 2 What is the value of X [#permalink]

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09 Mar 2015, 10:53
Don't look too far into this problem.

The main concept being tested here is the power of ZERO.

Any number raised to a zero power = 1. You should know this property and if you don't, use this as a learning opportunity.

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Re: 4^x + 4 ^-x = 2 What is the value of X   [#permalink] 09 Mar 2015, 10:53
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