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For how many integers n is 2^n = n^2 ?

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For how many integers n is 2^n = n^2 ?

by II » Sun Aug 24, 2008 2:57 pm
For how many integers n is 2^n = n^2 ?

A) None
B) One
C) Two
D) Three
E) More than Three

Please illustrate your thinking and how you would approach this question. Thanks.
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by carefreeamit » Sun Aug 24, 2008 4:22 pm
I think answer is C.
I can think of 2^2 and 2^4 after which 2^n becomes larger than n^2.
Correct me if I am wrong.[/spoiler]
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by II » Sun Aug 24, 2008 5:35 pm
carefreeamit wrote:I think answer is C.
I can think of 2^2 and 2^4 after which 2^n becomes larger than n^2.
Correct me if I am wrong.[/spoiler]
Yes ... that is also the way I did it ... but was thinking whether there are other approaches someone would use if this was a harder question.
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