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prove log_2 n^2 = little o(log_2 n^3) without using limits

prove log_2 n^2 = little o(log_2 n^3) without using limits

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Answer #1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

Let f(n)=log2(n^2) and g(n)=log2(n^3)

So, f(n) can be written as

f(n)=2*log2(n) (Using log properties)

g(n)=3*log2(n) (Using log properties)

So,

f(n)<=(3/2)*g(n)

So, we can choose any constant c>3/2

So, f(n)<c*g(n)

where c>3/2 be it c=2

So,

f(n)=o(g(n)) using the little o definition

Kindly revert for any queries

Thanks.

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