Asymptotic functions

Question

When can i used logarithms to compare two functions asymptotically?

What is the procedure and rules?

If we have n^2 ans n^3..if we compare using logarithms..thwn they tuen out to be asymptotically equal.should i then compare them by "not" ignoring the constant terms?.

Answer 1

Remember befor apllying log cancle common terms in funtions. otherwise it leads wrong answer.

Example: n³ , n² so on take log both given O(logn). 

But correct method is cancle common terms = n² then take see n s always greter than 1 so n³ is greater than n².

Comments

If there is no common factor..even then can i get a case where log comparision wont work ?

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if you talk about 2ⁿ and 3ⁿ since it is seen 3ⁿ  is always greater than appling log is wrong

give me case i will tell u based on that how we do .

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I dont have. Case..i just wanted to know the general way of solving usimg logarithms.

So if i get 2 functions as asymptotically equal in logarithms..then should i discard solving it and use another approach?..or should i consider the value of constants as well.

For ex..for 2^n and 3^n...on applying log..we get log2*logn...and log3*logn...so in this case..should solve usingsome.other method?..or sincr log2<log3..i should consider 2^n as O(3^n)

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