Question

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Answer 1

Explicație pas cu pas:

a)

${2}^{30} = {2}^{3 \cdot 10} = {( {2}^{3} )}^{10} = {8}^{10} \\ {3}^{20} = {3}^{2 \cdot 10} = {( {3}^{2} )}^{10} = {9}^{10}$

${8}^{10} < {9}^{10} \implies {2}^{30} < {3}^{20}$

b)

${5}^{34} = {5}^{2 \cdot 17} = {( {5}^{2} )}^{17} = {25}^{17} \\ {3}^{51} = {3}^{3 \cdot 17} = {( {3}^{3} )}^{17} = {27}^{17}$

${25}^{17} < {27}^{17} \implies {5}^{34} < {3}^{51}$

c)

${2}^{155} = {2}^{5 \cdot 31} = {( {2}^{5} )}^{31} = {32}^{31} \\ {3}^{93} = {3}^{3 \cdot 31} = {( {3}^{3} )}^{31} = {27}^{31}$

${32}^{31} > {27}^{31} \implies {2}^{155} > {3}^{93}$

e)

${10}^{74} = {10}^{2 \cdot 37} = {( {10}^{2} )}^{37} = {100}^{37}$

${6}^{123} = {6}^{3 \cdot 41} = {( {6}^{3} )}^{41} = {216}^{41}$

$100 < 216$

$37 < 41$

$\implies {100}^{37} < {216}^{41} \implies {10}^{74} < {6}^{123}$