but these two functions let us compare which one is greater so for this I will apply log on both sides so this is log of n bar log n and this is log off to power through 10 now this power comes out by a plane third formula so this becomes log n into log in so that our game decides for that slogan and all the DS logon and this power come to this side so root n log 2 base 2 this is one normal is this long square and this is 10 which one is bigger if you are unable to judge it still you can apply long directly write down and if I apply log then this will become 2 log of log n and this becomes this is and ball right so 1 by 2 log n now tell me which one is a smaller now off log n is a smaller than log n yes this is a smaller than that one but up like logs for one time if you are unable to judge it then you can apply log again and you can change it so here the thing is we have to judge which one is is smaller which one is greater so for making it easy we are applying long there is no rule there is no formula right just apply those so that you can reduce it and see and you can easily compare them so here me one time applying even unable to do it so it is I mean again the sphere as their log square and maybe then because this is square so just apply down one more time so you got love of love and that is just full of it so login is greater than log of love now let us see who is there dead to functions applying all log n into log of 2 days 2 this is 1 and this is root n log n so what's the answer here just log in and this is who can log in this is greater so this is small F all fairness to ng of an Austrian which is smaller which is greater Bhutan equal both are equal the stew is ignorable 3 is ignorable when you take it asymptotically big often we both had not heat off and knock it off both are same both are equal both these functions are equal now this function is greater this looks smaller this was taken let's go play God long two more hands log 2 ball 2 n so this n comes this side log 2 raised to this is 1 & 2 n come this side log boobies - this is fun now which is greater now don't say they are equal don't say they are equal we have a polite log and then we are combining them now I cannot say ignore that to directly the functions you can do that now for comparison purpose we already applied log so you cannot strike away the coefficient so this is to 1 that is greater and this is smaller so yes this function is small that function is greater you can clearly see from here only now I have taken this example to make you understand after a Blaine block don't cut off coefficients don't get out there ready in one of the example I give that but that time I did not apply longer no-till applied longer and have changed the functions knowing fricative coefficient it will be different outside it will be wrong answer directly from the functions you can set of coefficients so a plane log this to n is greater than n so that is greater actually this is for power and this is for power and this is greater than this one example let us compare two functions G 1 and G 2 which one is greater now here it is not a single expression here is n cube or n square so for any value less than infinity it is an Q after that it is n square so this is reducing and this is n square up to 10,000 after that this is n cube if I take n values let us say this is finite and this is N and this is 10,000 on this side who is greater the side less than 100 G 1 is greater and from hundred to 10,000 who is greater because the figures are there so I have used this on the bar now from hundred to 10,000 was later see 102 from hundred onwards this is just n square the square and below 10,000 also this is also n square so this one same square so both are n square so G 1 is equal to 0 here g---men was greater than 0 but beyond 10,000 beyond 10000 so 10,000 reason squared only after 10000 this is Thank u so G Poulos greater than Jima so this is still there this is infinity now who is the creator which function is greater Jeeva not G 2 G 2 is greater always from what value of n from 10000 onwards it's always greater before 10,000 they were changing their sights sometime this was their tower they were equal but from that point onwards 10000 onwards always G 2 is greater so cheapo is greater than G 1 G 2 is greater than G 1 so remember this so whenever you say some function is greater than other function you don't have to take those small values of n it can be from very large values of n also but from that point if it is always greater than we consider that function is greater all right we don't just check into smaller values and decide for all the values of n we decide means up to infinity so from composite may be there is no limit there's Monument so G 2 is always greater than 0 here's some asymptotic notations are given and compositions there so we have to find out whether these statements are true or false let us check this endless scheme whole poem and if you open this binomial right two terms are there so if you open this it will be n power n that is going to be a higher strong it is just like for example n plus 3 whole square then what is the highest at all you get there n square is not yet strong so if M is there as a power so n power n is very strong so he can write this have theta of M square yes it is exhibited often square so this is Theta of and is that mrs. Garrett then what about this one to power n plus 1 so this is 2 into coupon and to into group ahem coefficient is ignoring the analyst kicked off to war and also big also omegas anything you can write so this is also packed bigger its kind then let us take this one to raise to 2 to n as the story explained this is for power N and that is to pardon for more evidence greater than to pollen to pot and cannot be an upper bound for this one from so it should be big-oh of football not to worry this is wrong the next this one this is the Rudolph's login this is log of log n which one is greater you will play golf on both side and check it if you are playing along you get what one way to love of love it there log of log of log n still more smaller so that cannot be another bump this is greater value that's a smaller and smaller value cannot be an upper bound get this one if I have my log on both sides so this will be log n into log n so that is log square n and that is just n so that n is greater so yes this is the people this is big ol right so this is correct so that's it I have solved few problems using asymptotic notation so that you get the idea for what should be an approach for solving them and you have some examples these are the examples already have taken the example these are from some exams competitive exams so if you get any type of question now you will be able to solve it if you have practiced this little bit then you can solve any type of questions on asymptotic notation so here we end the first chapter of tell bottoms like if you take any textbook then or any university syllabus the first chapter is about algorithm their analysis and asymptotic notation so we have finished this so in the next videos you will find that second chapter onwards that is we will look at the strategies that is divided conquer and grading method these are strategies we will stop