2^2 = 2^2fangtray wrote:For how many integers n is 2^n = n^2
a. none
b. one
c. two
d. three
e. more than 3
2^4 = 4^2, So the answer should be [spoiler]C = 2[/spoiler]
Integer N
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neelgandham
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2^4 = 4^2, So the answer should be [spoiler]C = 2[/spoiler]
Anil Gandham
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We can solve this problem by trial and error method.
We will plug in values for n from 1,2,3,.... and chk for which value of n, 2^n = n^2.
1)n=1
2 = 1 FALSE
2)n=2
2^2 = 4; n^2 = 4 TRUE
3) n =3
2^3 = 8; 3^2 = 9 FALSE
4) n=4
2^4 = 16; 4^2=16 TRUE
5)n=5
2^5=32; 5^2=25 FALSE
6) n=6
2^6=64; 6^2 =36 FALSE
From this we can say that, as n increases, 2^n >> n^2.
hence for 2 values of n, this will hold true. SO the answer is option C
We will plug in values for n from 1,2,3,.... and chk for which value of n, 2^n = n^2.
1)n=1
2 = 1 FALSE
2)n=2
2^2 = 4; n^2 = 4 TRUE
3) n =3
2^3 = 8; 3^2 = 9 FALSE
4) n=4
2^4 = 16; 4^2=16 TRUE
5)n=5
2^5=32; 5^2=25 FALSE
6) n=6
2^6=64; 6^2 =36 FALSE
From this we can say that, as n increases, 2^n >> n^2.
hence for 2 values of n, this will hold true. SO the answer is option C
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Birottam Dutta
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In addition to the answers above, you may also draw a graph of the two functions 2^N and N^2 and see where they intersect. There will be two points which gives the answer to the question.
Hence, answer C.
Hence, answer C.
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