Hi,

I'd really appreciate some pointers on how to find the zeroes of the function ,

that is, for which .

I tried something along the lines of

but don't really know how to proceed from that.

Many thanks!

Printable View

- Apr 19th 2009, 04:27 AMgusztavFinding the zeroes of a function
Hi,

I'd really appreciate some pointers on how to find the zeroes of the function ,

that is, for which .

I tried something along the lines of

but don't really know how to proceed from that.

Many thanks! - Apr 19th 2009, 04:56 AMstapel
I don't think the equation can be solved algebraically. I think you have to use numerical methods to find

*approximate*zeroes. - Apr 19th 2009, 05:07 AMMoo
Hello,

It is not possible to find the*exact*value for which it is 0.

Generally, equations involving both polynomials and logarithms are hard to handle.

You can use approximation methods (euler, bisection...) or find the derivative and study the function to get a general idea.

f is defined over (0,infinity)

so

this function is strictly increasing.

Limit to 0 is -infinity, f(1)=1/2

so there is a unique value a for which f(a)=0 and a is in (0,1)

but if you can find c and d such that f(c)<0 and f(d)>0, then for sure, a is between c and d.