Hi there,

Given the following, I am wondering if it possible to express $x$ in terms of $a, b, c$ and $d$?

$\displaystyle ax+b+x^c=d$
$\displaystyle a,b,c \in (0,1)$
$\displaystyle d>0$
$\displaystyle x \leq d$
$\displaystyle 0 \leq x \leq 1$

I've tried messing around with the natural logarithm and exponential functions but to no avail, so far. I can solve by iteration if given values for a, b, c and d but can I express it as a closed formula?

Any help would be massively appreciated, thanks!