Question

Ordonati crescător numerele :
a) 5^300 ; 3^400 ; 8^200 ;
b) 2^60 ; 3^45 ; 5^30 ;
c) 32^25 ; 4^62 ; 64^21

Dau coroană.

Answer 1

rezolvarea in atasament.

Answer 2

   
[tex]a)\\ \text{Le aducem pe toate la puterea 100.}\\\\ 5^{300} = 5^{3\times100} = \Big(5^3\Big)^{100} =125^{100}\\\\ 3^{400} = 3^4\times100 = \Big(3^4\Big)^{100} = 81^{100}\\\\ 8^{200}=8^{2\times 100}= \Big(8^2\Big)^{100}=64^{100}\\\\ \text{Ordinea crescatoare este:}\\ 64^{100};~81^{100};~125^{100}~~\Longleftrightarrow~~8^{200};~3^{400};~5^{300}[/tex]


[tex]b)\\ \text{Le aducem pe toate la puterea 15.}\\\\ 2^{60} =2^{4\times 15} =\Big(2^4\Big)^{15} =16^{15} \\\\ 3^{45} =3^{3\times 15} =\Big(3^3\Big)^{15} =27^{15} \\\\ 5^{30}=5^{2\times 15} =\Big(5^2\Big)^{15} =25^{15} \\\\ \text{Ordinea crescatoare este:}\\ 16^{15};~25^{15};~27^{15}~~\Longleftrightarrow~~2^{60};~5^{30};~3^{45} [/tex]


[tex]c)\\ \text{Le aducem pe toate la baza 2.}\\\\ 32^{25}=\Big(2^5\Big)^{25}=2^{5\times25}=2^{125}\\\\ 4^{62}=\Big(2^2\Big)^{62}=2^{2\times62}=2^{124} \\\\ 64^{21}=\Big(2^6\Big)^{21}=2^{6\times21}= 2^{126}\\\\ \text{Ordinea crescatoare este:}\\ 2^{124} ;~2^{125};~2^{126}~~\Longleftrightarrow~~4^{62};~32^{25};~64^{21}[/tex]