Question

comparați numerele:
b)5³⁴ și 3⁵¹
c)2¹⁵⁵ și 3⁹³​

Answer 1

 

$\displaystyle\bf\\Comparati~numerele\!:\\\\b)\\5^{34}~si~3^{51}\\5^{34}=5^{2\times17}=\Big(5^2\Big)^{17}=25^{17}\\3^{51}=3^{3\times17}=\Big(3^3\Big)^{17}=27^{17}\\25^{17}<27^{17}\\\implies5^{34}<3^{51}\\\\\\c)\\2^{155}~si~3^{93}\\2^{155}=2^{5\times31}=\Big(2^5\Big)^{31}=32^{31}\\3^{93}=3^{3\times31}=\Big(3^3\Big)^{31}=27^{31}\\32^{31}>27^{31}\\\implies 2^{155}>3^{93}$