Looking for help reducing natural logarithm inequalities

• Sep 27th 2011, 05:38 PM
apritchard
Looking for help reducing natural logarithm inequalities
Graduate computer science student here, finding I've forgotten an awful lot of math. Ugh.

I'm trying to find the point at which 10n^2 surpasses the value of 300 ln n.

So:
10n^2 > 300 ln n
n^2 > 30 ln n

next: ??

I've tried reducing it as:

(n^2)/30 > ln n
e^((n^2)/30) > n

But then I'm not really sure where to go from there either. I just don't really remember how to approach this problem. I've been muddling over various ways to reduce logs and get all the variables grouped together, but nothing is jumping out at me. Any tips appreciated.
• Sep 27th 2011, 06:13 PM
skeeter
Re: Looking for help reducing natural logarithm inequalities
$\displaystyle \frac{n^2}{30} > \ln{n}$

$\displaystyle \frac{n^2}{30} - \ln{n} > 0$

graph $\displaystyle y = \frac{x^2}{30} - \ln{x}$ and look for x-values where y > 0
• Sep 27th 2011, 06:21 PM
apritchard
Re: Looking for help reducing natural logarithm inequalities
Thanks, Skeeter. That seems effective. Is there any way to reduce the problem to a solvable state, or is graphing it pretty much the way to go for getting a hard number?
• Sep 27th 2011, 06:47 PM
skeeter
Re: Looking for help reducing natural logarithm inequalities
you won't be able to solve the inequality using elementary algebraic methods ... there are some who frequent this site who could make a clever comparison using associated functions.

my advice is to make use of technology ... that's what it's designed for