I would like to solve for $x$ in the equations
$a=e^{-x}(m(1+x+x^2/2+x^3/3)-x^3/3)$
and
$a=e^{-x}(m(1+x+x^2/2+x^3/3+x^4/4)-x^4/4)$
or even with more terms. Here $a$ is some constant.
Does anyone have a hint?
I would like to solve for $x$ in the equations
$a=e^{-x}(m(1+x+x^2/2+x^3/3)-x^3/3)$
and
$a=e^{-x}(m(1+x+x^2/2+x^3/3+x^4/4)-x^4/4)$
or even with more terms. Here $a$ is some constant.
Does anyone have a hint?
Even the simpler problem $a=e^{-x}(m(1+x)-x)$ (assuming $m\ne1$) can only be solved for $x$ by introducing the Lambert $W$-function, which you are invited to look up.