If $${\text{lo}}{{\text{g}}_8}{\text{p}} = 25$$   and $${\text{lo}}{{\text{g}}_2}{\text{q}} = 5,$$   then -

$$\eqalign{ & {\text{lo}}{{\text{g}}_8}{\text{p}} = 25\,\,{\text{and lo}}{{\text{g}}_2}{\text{q}} = 5\, \cr & \Rightarrow {\text{p = }}{{\text{8}}^{25}}\,{\text{and q}} = {2^5} \cr & \Rightarrow {\text{p = }}{\left( {{2^3}} \right)^{25}}{\text{ and q = }}{2^5} \cr & \Rightarrow {\text{p = }}{{\text{2}}^{75}}{\text{ and q = }}{2^5} \cr & \Rightarrow {\text{p = }}{\left( {{2^5}} \right)^{15}}{\text{ and q = }}{2^5} \cr & \Rightarrow {\text{ p = }}{{\text{q}}^{15}} \cr} $$