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26 Jun 2024, 01:30
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B
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Difficulty:
15%
(low)
Question Stats:
80% (00:57) correct
20%
(00:49)
wrong
based on 117
sessions
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If \(x\) non-zero integer, how many values of \(x\) are there such that \((|x|)^x = 4\)?
A. None
B. 1
C. 2
D. 3
E. Infinitely many
A. None
B. 1
C. 2
D. 3
E. Infinitely many
06 Jul 2024, 09:30
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Official Solution:
If \(x\) non-zero integer, how many values of \(x\) are there such that \((|x|)^x = 4\)?
A. None
B. 1
C. 2
D. 3
E. Infinitely many
If \(x < 0\), then we'd have \((-x)^x = 4\). No negative integer satisfies this equation because \((-x)^x = (positive \ integer)^{(negative \ integer)}\) is less than or equal to 1 (\((-x)^x = (positive \ integer)^{(negative \ integer)}\) would be \(1, \ \frac{1}{4}, \ \frac{1}{27}, \ ...\)).
If \(x > 0\), then we'd have \(x^x = 4\). This yields \(x = 2\).
Therefore, \(x\) could only be 2.
Answer: B
If \(x\) non-zero integer, how many values of \(x\) are there such that \((|x|)^x = 4\)?
A. None
B. 1
C. 2
D. 3
E. Infinitely many
If \(x < 0\), then we'd have \((-x)^x = 4\). No negative integer satisfies this equation because \((-x)^x = (positive \ integer)^{(negative \ integer)}\) is less than or equal to 1 (\((-x)^x = (positive \ integer)^{(negative \ integer)}\) would be \(1, \ \frac{1}{4}, \ \frac{1}{27}, \ ...\)).
If \(x > 0\), then we'd have \(x^x = 4\). This yields \(x = 2\).
Therefore, \(x\) could only be 2.
Answer: B
General Discussion
26 Jun 2024, 03:13
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Here x is a non zero integer
x can be either +-2
however since it is raised to itself -2^-2 isnt 4 so hence only 1 such value for x exists-> B
x can be either +-2
however since it is raised to itself -2^-2 isnt 4 so hence only 1 such value for x exists-> B
