va rog exercitiul 1 ,2 si 7 dau mai mult de 30 de puncte si o coroana

1. a) [tex] 4^{17} = (2^{2})^17= 2^{34} [/tex]
b).[tex] 3^{27} \ \textgreater \ 3^{26} [/tex]
c)[tex] 49^{18} = (7^{2})^18= 7^{36} \ \textgreater \ 7^{35} [/tex]
d)[tex] 2^{51} \ \textgreater \ 2^{52} [/tex]
e)[te] 64^{17}= (8^{2} )^17= 8^{34} [/tex]
g)[tex] 100^{10} = (10^{2})^10= 10^{20} \ \textless \ 10^{100} [/tex]).
3. a) [tex] 2^{35} = 2^{35}[/tex]
[tex] 4^{18} = (2^{2})^18= 2^{36}
8^{11}= (2^{3})^11 = 2^{33}
8^{11} \ \textless \ 2^{35} \ \textless \ 4^{18} [/tex]
c) [tex] 5^{39} \ \textless \ 25^{20} \ \textless \ 125^{14} [/tex]
7. b) y=8x(7+5-4)=[tex] 8^{2}= 4^{3} [/tex]
c) z=27x(95-68)=[tex] 27^{2}= 3^{6}= (3^{2})^3= 9^{3} [/tex]
f). v=[tex] 2^{61}- 2^{60} = (2^{30)^2}= (2^{20})^3[/tex]
g). w=[tex] 3^{37}-2x 3^{36}= (3^{18})^2= (3^{12})^3 [/tex]
i). r=[tex]( 6^{7})^8 : 6^{2} = 6^{56} : 6^{2} = 6^{54} = (6^{18})^3 [/tex]

Macoveistefan Macoveistefan · Answer 2 · 2016-06-22T16:09:49+03:00

1.
__a) 4[tex] 4^{17} [/tex]=(2²)[tex] ^{17} [/tex]=[tex] 2^{34} [/tex]⇒[tex] 4^{17} [/tex]=[tex] 2^{34} [/tex]

__b)[tex] 9^{13} =(9^2)^13[/tex][tex]= 3^{26} [/tex]⇒[tex] 3^{27} [/tex]≥[tex] 9^{13} [/tex]

__c)[tex] 49^{18} =(7^2)^18[/tex]=[tex] 7^{36} [/tex]⇒[tex] 49^{18} \geq 7 ^{35} [/tex]

__d)[tex] 8^{17} =(2^{3} ) ^{17} [/tex]=[tex] 8^{51} [/tex]⇒[tex] 8^{17} \leq 2 ^{52} [/tex]

__e)[tex] 64^{17} =( 8^{2}) ^{17} =8^{34} [/tex]⇒[tex] 63^{17} =8^{34}[/tex]

__f)[tex] 81^{25} =(3^{4})^{25}=3^{100} [/tex]⇒ [tex] 81^{25} [/tex] [tex] 3^{100} [/tex]

__g)[tex] 100^{10} = (10^{2})^{10}=10^{20}[/tex]⇒[tex]100^{10} \leq 10^{100}[/tex]

_h)[tex] 27^{13} =(3^{3})^{13}=3^{39} ; 9^{20} =( 3^{2})^{20}=3^{60}[/tex] ⇒