[tex]\displaystyle\bf\\3^{34}=3^{2\times17}=\Big(3^2\Big)^{17}=9^{17}\\\\2^{51}=2^{3\times17}=\Big(2^3\Big)^{17}=8^{17}\\\\9^{17}>8^{17}\\\\\implies~~\boxed{\bf3^{34}>2^{51}}[/tex]
