Răspuns:
Explicație pas cu pas:
[tex]\bf 2^{30}=(2^3)^{10}=8^{10}[/tex]
[tex]\bf 3^{20}=(3^2)^{10}=9^{10} \implies \blue{\underline{~ 2^{30} ~< ~3^{20}}}[/tex]
[tex]\bf 5^{34}=(5^2)^{17}=25^{17}[/tex]
[tex]\bf 3^{51}=(3^3)^{17}=27^{17} \implies \green{\underline{~5^{34} ~< ~3^{51}}}[/tex]
[tex]\bf 2^{155}=(2^5)^{31}=32^{31}[/tex]
[tex]\bf 3^{93}=(3^3)^{31}=27^{31} \implies \purple{\underline{~3^{93}~ < ~2^{155}}}[/tex]
[tex]\bf 2^{111} \cdot 5^{38}=(2 \cdot5)^{38} \cdot 2^{73}=10^{38} \cdot2^{73}[/tex]
[tex]\bf 10^{38} \cdot2^{73}~ > ~3^{131} \implies \pink{\underline{~ 2^{111} \cdot 5^{38}~ > ~3^{131}}}[/tex]
[tex]\bf 10^{74}=(10^2)^{37}=100^{37}[/tex]
[tex]\bf 6^{123}=(6^3)^{41}=216^{41}\implies \red{\underline{~100^{37}~ < ~216^{41}}}[/tex]
[tex]==pav38==[/tex]