Numerically solve the equation
1/N/(Exp[-a[x]] - 1) == 1 - PolyLog[3/2, a[x]]*x^3
and plot a[x] for N = 100, 10^5 and 10^9.
I know how to solve numerically when I'm trying to get a number (e.g. solve Exp[x]==Sin[x] for x), but not when I want a function.
How can this be done?