Solving for $a$ (log probably required) I need to get $c$ in terms of $a$.
Both $c, a\in \Bbb R^+$
$$
c^{2a} = c/a 
$$
I'm pretty sure that log is required to solve this, but I'm not quite sure how to approach it.

Since $c>0$, we may divide both sides by $c$ to obtain:
$$
c^{2a-1} = \frac1a
$$
To undo the exponent, we raise both sides of the equation to the power of $\dfrac{1}{2a-1}$ to obtain:
$$
c= \left(\frac1a\right)^{\dfrac{1}{2a-1}}
$$
