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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 --> \(4^x=1\) --> \(x=0\);

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

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25 Jun 2013, 12:41

3

This post received KUDOS

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

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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