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78% (00:44) correct
22%
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For how many integers n is 1^n = n^1?
A. none
B. 1
C. 2
D. 3
E. More than 3
A. none
B. 1
C. 2
D. 3
E. More than 3
My answer was d. 3 because:
1^0 = 0^1 = 1
1^-1 = -1^1
and 1^1 = 1^1
Hence we have 3 integers for this, but the answer was given as b. 1 saying that 1^1 = 1^1 (n=1).
1^0 = 0^1 = 1
1^-1 = -1^1
and 1^1 = 1^1
Hence we have 3 integers for this, but the answer was given as b. 1 saying that 1^1 = 1^1 (n=1).
28 Dec 2011, 01:02
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Also, I would like to know the answer when we change the question as:
1. 2^n = n^2 (how many integers will satisfy this?)
2. 3^n = n^3 (how many integers will satisfy this?)
Many thanks,
1. 2^n = n^2 (how many integers will satisfy this?)
2. 3^n = n^3 (how many integers will satisfy this?)
Many thanks,
28 Dec 2011, 01:04
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vix,
0^1 is 0, not 1, so your first equation does not hold
-1^1 is -1, not 1, so your second equation does not hold either
Only n=1 satisfies the equation, so the answer is (B)
0^1 is 0, not 1, so your first equation does not hold
-1^1 is -1, not 1, so your second equation does not hold either
Only n=1 satisfies the equation, so the answer is (B)
