$\begin{align}  & {{\log }_{10}}45={{\log }_{10}}9+{{\log }_{10}}5 \\ & {{\log }_{10}}45={{\log }_{10}}{{3}^{2}}+({{\log }_{10}}10-{{\log }_{10}}2) \\ & {{\log }_{10}}45=2{{\log }_{10}}3+(1-{{\log }_{10}}2) \\ & {{\log }_{10}}45=2(0.4771)+(1-0.3010) \\ & {{\log }_{10}}45=0.9542+0.6990=1.6532 \\\end{align}$