Finding membrane potential equation using the Nernst equation?
The Nernst Equation is $E = E^\circ - \frac{RT}{nF} \ln{Q_c}$. From that you can derive the approximation you gave. $Q_c$ is the product of the activities of the products over those of the reactants. This can be, for dilute solutions where activity approximates concentration, the typical [B]/[A] for the reaction A→B. So, the only thing you need to "explain" is why E° would be zero. Review the definition of E°.  hint:What is ln(1/1)? See the discussion on concentration cells in:  http://www.chem1.com/acad/webtext/elchem/ec4.html