Question

Sa se compare :

${4}^{56} \: cu \: {4}^{78}$
${3}^{84} \: cu \: {5}^{96}$
${7}^{48} \: cu \: {5}^{48}$
${8}^{65} \: cu \: {4}^{98}$
Va rog rezolvati repede, dau coroana! ​

Answer 1

 

$\displaystyle\bf\\Sa~se~compare:\\\\4^{56}~cu~4^{78}\\4=4\\56<78\\\implies4^{56}<4^{78}\\\\\\3^{84}~cu~5^{96}\\3<6\\84<96\\\implies3^{84}<5^{96}\\\\\\7^{48}~cu~5^{48}\\7>5\\48=48\\\implies7^{48}>5^{48}\\\\\\8^{65}~cu~4^{98}\\\\\Big(2^3\Big)^{65}~cu~\Big(2^2\Big)^{98}\\\\2^{3\times65}~cu~2^{2\times98}\\2^{195}~cu~2^{196}\\2=2\\195<196\\\implies2^{195}<2^{196}\\\implies8^{65}<4^{98}$