$\begin{align}  & x{{\log }_{16}}N={{\log }_{2}}N \\ & x{{\log }_{{{2}^{4}}}}N={{\log }_{2}}N\text{  }\left| \text{Note: }{{\log }_{{{a}^{z}}}}b=\tfrac{1}{z}{{\log }_{a}}b \right. \\ & \frac{x}{4}{{\log }_{2}}N={{\log }_{2}}N \\ & \frac{x}{4}=1;\text{  }x=4 \\ & {{\log }_{5}}N+{{\log }_{25}}N=6 \\ & {{\log }_{5}}N+{{\log }_{{{5}^{2}}}}N=6 \\ & {{\log }_{5}}N+\tfrac{1}{2}{{\log }_{5}}N=6\left| {{\log }_{{{a}^{z}}}}b=\tfrac{1}{z}{{\log }_{a}}b \right. \\ & \tfrac{3}{2}{{\log }_{5}}N=6 \\ & {{\log }_{5}}N=4 \\ & N={{5}^{4}}=625 \\\end{align}$