(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to find n such that,

[tex]y=\frac{ln(cos(x))}{cos(1)}-x^n[/tex]

is zero for all [tex]0\leq x\leq 1[/tex].

3. The attempt at a solution

I've already narrowed it down to [tex]2<n<2.5[/tex] and I understand that the answer will probably be an approximation. I'm hoping for an exact solution though, however ugly it may be.

Any ideas?

p.s. this isn't a homework problem, so it may well be that you can't have the function be zero for all x between 0 to 1 for any n. It seems as though for some n I've chosen, the function is always going to be under the x axis or above the x axis depending on my n. If it so happens that this is always the case even for n approaching very close to my desired value, then my question should have a valid solution. I'm curious as to how I could show it is always above/below the axis for some n or if it isn't.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Function help.

**Physics Forums | Science Articles, Homework Help, Discussion**