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For how many integers n is 2^n = n^2 ?
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15 Dec 2022, 07:42
15 Dec 2022, 07:42
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Expert Reply
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Question Stats:
66% (00:52) correct
33% (00:40) wrong based on 3 sessions
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For how many integers n is 2^n = n^2?
A. None
B. One
C. Two
D. Three
E. More than Three
A. None
B. One
C. Two
D. Three
E. More than Three
Re: For how many integers n is 2^n = n^2 ?
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16 Dec 2022, 23:41
16 Dec 2022, 23:41
Expert Reply
\(2^n= n^2\) is true for 2 integers:
\(n=2\) --> \(2^2=2^2=4\);
\(n=4\) --> \(4^2=2^4=16\).
Well, \(2^2=2^2=4\) is obvious choices, then after trial and error you'll get \(4^2=2^4=16\) as well. But how do we know that there are no more such numbers? You can notice that when \(n\) is more than 4 then \(2^n\) is always more than \(n^2\) so \(n\) cannot be more than 4. \(n\) cannot be negative either as in this case \(2^n\) won't be an integer whereas \(n^2\) will be.
Answer: C.
\(n=2\) --> \(2^2=2^2=4\);
\(n=4\) --> \(4^2=2^4=16\).
Well, \(2^2=2^2=4\) is obvious choices, then after trial and error you'll get \(4^2=2^4=16\) as well. But how do we know that there are no more such numbers? You can notice that when \(n\) is more than 4 then \(2^n\) is always more than \(n^2\) so \(n\) cannot be more than 4. \(n\) cannot be negative either as in this case \(2^n\) won't be an integer whereas \(n^2\) will be.
Answer: C.
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Re: For how many integers n is 2^n = n^2 ?
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14 Jan 2023, 22:51
14 Jan 2023, 22:51
1
\(2^n\) = \(n^2\) for two values of n
n = 2
\(2^2\) = \(2^2\) = 4 and
and n = 4
\(2^4\) = \(4^2\) = 16
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Exponents
n = 2
\(2^2\) = \(2^2\) = 4 and
and n = 4
\(2^4\) = \(4^2\) = 16
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Exponents
