$\begin{align}  & \overbrace{{{a}^{2}}+{{b}^{2}}}^{{{(a+b)}^{2}}-2ab}=23ab \\ & {{(a+b)}^{2}}-2ab=23ab \\ & {{(a+b)}^{2}}=25ab \\ & \frac{{{(a+b)}^{2}}}{25}=ab \\ & {{\left( \frac{a+b}{5} \right)}^{2}}=ab \\ & \text{Take the log of both sides} \\ & \text{log}{{\left( \frac{a+b}{5} \right)}^{2}}=\log ab \\ & 2\log \left( \frac{a+b}{5} \right)=\log a+\log b \\ & \log a+\log b=2\log \left( \frac{a+b}{5} \right) \\\end{align}$