Is it possible to solve the following equation analytically for r:
$$A = exp\bigg[a\bigg(\frac{r}{r_{0a}}\bigg)^b\bigg] + exp\bigg[c\bigg(\frac{r}{r_{0c}}\bigg)^d\bigg] + exp\bigg[f\bigg(\frac{r}{r_{0f}}\bigg)^g\bigg] $$
Where every quantity is known except for r? I can't figure it out, and I don't think it is. Any idea how accurate a first order Taylor expansion would be?