Solving a logarithmic polynomial
I want to solve this equation for :
Is there a closed form for it, or does it have to be solved numerically? I can turn it in to this:
Which is in a form similar to , which is a deceptively simple equation that I don't know how to solve analytically. It feels very similar to a polynomial, but instead of powers of it's increasing
Failing a closed form answer, is there a useful closed form bound?