For which values of n does equation 2 become smaller than equation 1?

Please allow me to introduce myself; Name is Morris, I am a computer programmer.

For which values of n does equation 2 become smaller than equation 1?

1. 8(n^2)

2. 64 n (log n to base 2)

Show clear working please.

Re: For which values of n does equation 2 become smaller than equation 1?

Quote:

Originally Posted by

**mmwanga** Please allow me to introduce myself; Name is Morris, I am a computer programmer.

For which values of n does equation 2 become smaller than equation 1?

1. 8(n^2)

2. 64 n (log n to base 2)

Show clear working please.

1. I assume that you want to solve for n the inequality

$\displaystyle 8n^2 < 64 n \log_2(n)$

2. What kind of number is n? Real or natural? I'm going to use real numbers!

3. It is a little bit easier to solve the equation

$\displaystyle 8n^2 = 64 n \log_2(n)$

for n, but I doubt that you can solve this equation algebraically. So use a numerical iterative method.

With Newton's method you'll get $\displaystyle n \approx 1.099997$

4. To answer your question: For $\displaystyle n \in (0, 1.099997)$ the 2nd term is smaller than the 1st one.

Re: For which values of n does equation 2 become smaller than equation 1?

Thank you for this answer. Would this wolfram alpha plot accurately represent this solution?

http://www.wolframalpha.com/input/?i=plot+8+x+^+2+%2C+64+x+log+[2%2Cx]%2C+x%3D0+to+2

In Wolfram alpha : plot 8 x ^ 2 , 64 x log [2,x], x=0 to 2

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Re: For which values of n does equation 2 become smaller than equation 1?

Quote:

Originally Posted by

**mmwanga** Thank you for this answer. Would this wolfram alpha plot accurately represent this solution?

...

1. Yes

2. I would use a slightly different scaling of the axes such that you can read the coordinates of the point of interception. (see attachment)

Re: For which values of n does equation 2 become smaller than equation 1?

Thank you! Using a different scale definitely makes it more

Re: For which values of n does equation 2 become smaller than equation 1?