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

• Oct 26th 2012, 09:00 AM
mmwanga
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)

• Oct 26th 2012, 10:47 AM
earboth
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)

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

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

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

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

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 $n \approx 1.099997$

4. To answer your question: For $n \in (0, 1.099997)$ the 2nd term is smaller than the 1st one.
• Oct 26th 2012, 12:41 PM
mmwanga
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
• Oct 27th 2012, 12:07 AM
earboth
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)
• Oct 27th 2012, 05:18 AM
mmwanga
Re: For which values of n does equation 2 become smaller than equation 1?
Thank you! Using a different scale definitely makes it more
• Oct 27th 2012, 08:51 AM
ujgilani
Re: For which values of n does equation 2 become smaller than equation 1?