Electrolyte solutions

Dissociating $n_i$ moles $M_{\nu_+}X_{\nu_-}$ we get: \begin{equation} n_+=\nu_+n_i\;\;\;\Rightarrow \;\;\; m_+=\nu_+ m_i \end{equation} \begin{equation} n_-=\nu_- n_i\;\;\;\Rightarrow \;\;\; m_-=\nu_- m_i \end{equation} Substituting into equation (61) \begin{equation} \mu_i=\mu_{i}^{0}+RTln\left[\gamma_{\pm}^{\ nu}\left(\frac{\nu_{+}m_i}{m^0}\right)^{\nu_+}\left(\frac{\nu_-m_i}{m^0}\right)^{ \nu_-}\right] \end{equation} Grouping Terms \begin{equation} \mu_i=\mu_{i}^{0}+RTln\left[\gamma_{\pm}^{\nu}\nu_{ \pm}^{\nu}\left(\frac{m_i}{m^0}\right)^{\nu}\right] \end{equation} Applying properties of natural logarithms. \begin{equation} \mu_i=\mu_{i}^{0}+\nu RTln\left[\gamma_{\pm}\nu_{\pm}\left(\frac{m_i}{m^{0} }\right)\right] \end{equation}