solving quadratic equation involving log

Hi,

How do you solve an equation with a quadratic expression on one side and a log expression on the other?

The specific question is:

2*n*log10(n) = 0.1*n^2

(Background: this is actually for an algorithm analysis question - I am trying to find the intersection points of the worst-case running times of two algorithms)

Thanks

Re: solving quadratic equation involving log

Well if you write this as

Since is undefined, we can't accept as a solution, which means we have

You will need to use a numerical method to solve this.

Re: solving quadratic equation involving log

This is a tricky one, but maybe we can work it around a bit so the solution might be easier to find.

You can solve it numerically from here.

Re: solving quadratic equation involving log

Thanks a lot for the fast replies.

I also got up to n = 10^(0.05*n) and did not know how to proceed any further. What is meant by solving it numerically, exactly? Does it basically mean a brute-force approach?

Cheers

Re: solving quadratic equation involving log

Yep, brute force, open up a spreadsheet you'll find

Re: solving quadratic equation involving log