Question:

Given <span class="math-inline">\log_{a} = p = \log_{b}q</span> and <span class="math-inline">\log_{b}q = \frac{2}{p}</span>. If <span class="math-inline">\log_{g}(\frac{a^{4}b^{3}}{c}) = \alpha p^{3} + \beta p^{2} + \gamma p + \delta (\forall p \in R - \{0\})</span>, then <span class="math-inline">(\alpha + \beta + \gamma)</span> equals -