So sánh 2 biểu thức: 2^ 30 + 3^ 30 + 4 ^30 và 3 . 24 ^10 .
Giải thích
Ta có: \({4^{30}} = {2^{30}}{.2^{30}} = {\left( {{2^3}} \right)^{10}}.{\left( {{2^2}} \right)^{15}} = {8^{10}}{.4^{15}}\).
Mà \({8^{10}}\,\,.\,\,{4^{15}} > {8^{10}}\,\,.\,\,{3^{15}} > {8^{10}}\,\,.\,\,{3^{11}} > {8^{10}}\,\,.\,\,{3^{10}}\,\,.\,\,3 = {\left( {8\,\,.\,\,3} \right)^{10}}\,\,.\,\,3 = {24^{10}}\,\,.\,\,3\).
Vì \[{4^{30}} > 3\,\,.\,\,{24^{10}}\] nên \({2^{30}} + {3^{30}} + {4^{30}} > 3\,\,.\,\,{24^{10}}\).