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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, 23:30
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A
B
C
D
E

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80% (01:10) correct 20% (01:08) wrong based on 205 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, 04:00
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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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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, 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
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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, 05:02
Thanks ! I love this method :
4^0+4^0=1+1=2 Ans. C
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could someone explain me step by step how to solve this kind of questi  [#permalink]

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

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

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

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New post 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.
Or follow ZONEF preference method.
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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 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
Answer C.

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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