Răspuns:
Explicație pas cu pas:
semnele ≤ și ≥ sunt, de fapt, stricte (fără egal).
scuze pentru ultimul exercițiu, ca nu l-am finalizat.
[tex]2^{53} \\4^{29} =(2^{2}) ^{29} = 2^{58}\\2^{53} \leq 2^{58}[/tex]
[tex]9^{51} = (3^{2})^{51}= 3^{102}\\3^{103}\geq 3^{102}[/tex]
[tex]4^{37} = (2^{2})^{37} = 2^{74}\\8^{31} = (2^{3})^{31} = 2^{62}\\2^{74}\geq 2^{62}[/tex]
[tex]9^{24} = (3^{2})^{24}= 3^{48}\\27^{16} = (3^{3})^{16}= 3^{48}\\\\9^{24} = 27^{16}[/tex]
[tex]125^{43}= (5^{3})^{43}=5^{129}\\25^{61}= (5^{2})^{61}=5^{122}\\125^{43}\geq 25^{61}[/tex]
[tex]10^{43} \\100^{19} = (10^{2})^{19}= 10^{38}\\10^{43}\leq 100^{19}[/tex]
[tex]2^{30}= (2^{3})^{10}= 8^{10}\\3^{20}= (3^{2})^{10}= 9^{10}\\2^{30}\leq 3^{20[/tex]
[tex]5^{34} = 5^{2*17}= (5^{2})^{17}=25^{17}\\3^{51} = 3^{3*17}= (3^{3})^{17}=27^{17}\\5^{34}\leq 3^{51}[/tex]
[tex]2^{155}= 2^{5*31}=(2^{5})^{31}= 32^{31}\\3^{39}= 3^{8+31}=3^{8}*3^{31}[/tex]
