Question

comparati numerele:2 la puterea 111x5 la puterea 38 si 3 la puterea131

Answer 1

$2^{111} * 5^{38} =2^{3*37} * 5^{2*19}=( 2^{3} )^{37} * ( 5^{2} )^{19}=8^{37}*25^{19}$

si

$3^{131} = 3^{74+57} =3^{2*37}*3^{3*19}=( 3^{2} )^{37} * ( 3^{3} )^{19}=9^{37}*27^{19}$

Cum
$8^{37}<9^{37}$

si
[tex] 25^{19}<27^{19}[/tex]

rezulta ca

$2^{111} * 5^{38} < 3^{131}$