詳解：根據對數律

\({{\rm{3}}^{{\rm{100}}}}{\rm{ = 1}}{{\rm{0}}^{\log {{\rm{3}}^{{\rm{100}}}}}} = {10^{100\log 3}} = {10^{47.71}} = {10^{0.71}} \cdot {10^{47}}\)

\(\because \) \({10^{0.4771}} \buildrel\textstyle.\over= 3\) , \({10^{0.6020}} \buildrel\textstyle.\over= 4\)  ,  \({10^{0.6990}} \buildrel\textstyle.\over= 5\)  ,  \({10^{0.7781}} \buildrel\textstyle.\over= 6\)

\(\therefore {10^{0.71}} \cdot {10^{47}} \buildrel\textstyle.\over= 5. \sim \times {10^{47}}\)

故為48位數，第一位數字為5