Please excuse me, this is my first time using the site and I have absolutely no idea what I'm doing with the notation. Anyways, I am attempting to prove that:
$$R_m = m\left(e^{\frac{R_c}{m}}-1\right)$$
Where...
$$R_c = m\left(ln\left({1+\frac{R_m}{m}}\right)\right)$$
$e^{\frac{m(ln(1+\frac{R_m}{m}))}{m}} \rightarrow e^{ln(1+\frac{R_m}{m})} \rightarrow 1+\frac{R_m}{m}$
Plugging it back into the larger equation
$m(1+\frac{R_m}{m}-1) \rightarrow R_m$