Arrange in increasing order of asymptotic complexity

Question

I have to arrange the above time complexity function in increasing order of asymptotic complexity and indicate if there exist functions that belong to the same order.

So, my answer is

$[lg(n)]^2$
$lg(2^n)$ and $log(2^n)$ and $2^{lg(n)}$ these belong to the same order of O(n)
$nlog(n) + 1000 $
$n^{1.1}$

Just wish to check whether i'm right, since I'm not getting the same result as others. Thanks.

Answer 1

I am familiar with the question. (I am one of the "others") I believe you neglected to specify that lg is log base 2.

In increasing order of asymptotic complexity:

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$lg^2(n) = O(lg^2(n))$

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$lg(2^n) = n = O(n)$

$log(2^n) = n * log(2) = O(n)$

$2^{lg(n)} = n = O(n)$

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$n*log(n)+1000 = O(n log(n))$

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$n^{1.1} = O(n^{1.1})$