Is there a property for log(n)/n? I found a small exercise which I couldn't figure what to do, so I found a solution. Then I tried to understand it and everything went well until I got to this part: 1/8=log(n)/n Then it just skipped and say that the answer was n=43. I was wondering if there is some kind of property for log(n)/n I don't know about. Or otherwise, how was this solved? EDIT: This is the exercise Suppose we are comparing implementations of insertion sort and merge sort on the same machine. For inputs of size n, insertion sort runs in 8n2 steps, while merge sort runs in 64n lg n steps. For which values of n does insertion sort beat merge sort?

przesypkai4 2022-07-17 Answered
Is there a property for log(n)/n?
I found a small exercise which I couldn't figure what to do, so I found a solution. Then I tried to understand it and everything went well until I got to this part:
1 8 = log ( n ) n
Then it just skipped and say that the answer was n = 43. I was wondering if there is some kind of property for log ( n ) / n I don't know about. Or otherwise, how was this solved?
EDIT: This is the exercise Suppose we are comparing implementations of insertion sort and merge sort on the same machine. For inputs of size n, insertion sort runs in 8n2 steps, while merge sort runs in 64n lg n steps. For which values of n does insertion sort beat merge sort?
And this was the solution given:
8 n 2 = 64 n log ( n )
n 2 = 8 n log ( n )
n = 8 log ( n )
1 8 = l o g ( n ) n
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

nezivande0u
Answered 2022-07-18 Author has 16 answers
If we take your amended question, which asks us to solve the inequality:
8 n 2 < 64 n log 2 ( n )
We can therefore divide both sides by 64 n to get:
n 8 < log 2 ( n )
This has to be solved by numerical methods and we see that we have (by Mathematica):
1.1 < n 43.5593
And we note that n must be an integer so we have:
1.1 = 2 < n < 43 = 43.5593

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-03-23

Limit with ' sequence and inverse logintegral
I found formula below
limnlim-1(n)pn=1
where lim-1(n) is inverse logintegral function and pn is ' number sequence.
Can anyone prove this formula?

asked 2022-05-13
What is the limit of difference between harmonic series and natural logarithm of n+1?
I'm an undergraduate student in geology and I'm dealing with a project in math. The last question of the project gives me the harmonic series ( A n = 1 + 1 2 + . . . + 1 n ) and this natural logarithm L = ln ( 1 + n ) and asks me to see what happens with the difference A n L when n . I've already done some symbolic computations in Matlab and the answer I get is "eulergamma". So, after some online research I found out that eulergamma is the Euler-Mascheroni constant (being 0.5772....). Not knowing too much about this, I answered the question as follows: "I notice that lim n ( A n L ) behave same as lim n ( A n ln ( n ) ) which is equal to Euler-Mascheroni constant. So, the requested difference A n L is equal to Euler-Mascheroni constant as n ."
Teacher asked me "Why does this A n L behave in the same way as this A n ln ( n )? Try to do something. Add/subtract ln ( n ) for example."
Afterall here I am and asking for your help. I tried to add/subtract ln ( n ) but nothing came up. Could you please help me with this, or at least give me some clues/hints? I don't have such an experience on this!!
Thank you for your attention!
asked 2022-09-24
Upperbound for i = 1 N a i ln a i
It's easy to prove that following upperbound is true:
i = 1 N a i ln a i A ln A, where i = 1 N a i = A and a i 1
I'm wondering, is there stronger upperbound?
asked 2022-03-26
Could you describe this function as "logarithmic"?
f(x)=1x
As x increases, the value of f(x) decreases, but the decrease tapers off quickly as x gets larger, and if you plot the graph of f(x), the shape looks kind of like an upside-down logarithm. Would it be correct to describe this function as declining logarithmically, as x increases?
asked 2022-07-12
Does n = 2 ( n ln n ) 1 diverge?
This seems like elementary calculus, but I can't figure this out. Can anyone supply a hint?
asked 2022-08-05
Suppose that In 2 = a and In 3 = b. Use properties of logarithms to write logarithm in terms of a and b.
ln 2 3 4
asked 2022-07-17
Find all a such that lim x ( x + a x a ) x = e
Saw this problem and I thought I'd take a shot at it:
Find all a such that
lim x ( x + a x a ) x = e .

New questions