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25 Jun 2024, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
59% (01:15) correct
41%
(01:10)
wrong
based on 272
sessions
History
Date
Time
Result
Not Attempted Yet
If \(x\) non-zero integer, how many values of \(x\) are there such that \((\frac{x}{2})^x = 1\)?
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, 08:30
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Official Solution:
If \(x\) non-zero integer, how many values of \(x\) are there such that \((\frac{x}{2})^x = 1\)?
A. None
B. 1
C. 2
D. 3
E. Infinitely many
Since \(x \neq 0\), for \((\frac{x}{2})^x = 1\) to hold true, the base (\(\frac{x}{2}\)) must be 1, and the exponent (\(x\)) can be any number (\(1^{anything} = 1\)) or the base (\(\frac{x}{2}\)) must be -1 and the exponent (\(x\)) must be even (\((-1)^{even} = 1\)).
If \(\frac{x}{2} = 1\), then \(x = 2\).
If \(\frac{x}{2} = -1\), then \(x = -2\), which is even.
Therefore, \(x\) could be 2 or -2.
Answer: C
If \(x\) non-zero integer, how many values of \(x\) are there such that \((\frac{x}{2})^x = 1\)?
A. None
B. 1
C. 2
D. 3
E. Infinitely many
Since \(x \neq 0\), for \((\frac{x}{2})^x = 1\) to hold true, the base (\(\frac{x}{2}\)) must be 1, and the exponent (\(x\)) can be any number (\(1^{anything} = 1\)) or the base (\(\frac{x}{2}\)) must be -1 and the exponent (\(x\)) must be even (\((-1)^{even} = 1\)).
If \(\frac{x}{2} = 1\), then \(x = 2\).
If \(\frac{x}{2} = -1\), then \(x = -2\), which is even.
Therefore, \(x\) could be 2 or -2.
Answer: C
General Discussion
25 Jun 2024, 02:59
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\((\frac{x}{2})^x= 1\)
simplifying this will give:
\(x^x=2^x\)
so \(x\) could be \(±2\)
There are 2 values that can satisfy the given condition
Hence C is the answer
simplifying this will give:
\(x^x=2^x\)
so \(x\) could be \(±2\)
There are 2 values that can satisfy the given condition
Hence C is the answer
