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.
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)
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.