Răspuns: Ai mai jos rezolvarea
Explicație pas cu pas:
Buna!
[tex]\bf a)~27^{30}= (3^{3})^{30}= 3^{3\cdot 30}=\boxed{\bf 3^{90}}[/tex]
[tex]\bf 9^{45}= (3^{2})^{45}= 3^{2\cdot 45}=\boxed{\bf 3^{90}}[/tex]
[tex]\bf \implies\boxed{ \boxed{\bf 3^{90}=3^{90}}}[/tex]
[tex]\it~~[/tex]
[tex]\bf b)~8^{20}= (2^{3})^{20}= 2^{3\cdot 20}=\boxed{\bf 2^{60}}[/tex]
[tex]\bf 4^{28}= (2^{2})^{28}= 2^{2\cdot 28}=\boxed{\bf 2^{56}}[/tex]
[tex]\bf \implies\boxed{ \boxed{\bf 2^{60}>2^{56}}}[/tex]
[tex]\it~~[/tex]
[tex]\it~~[/tex][tex]\bf c)~3^{40}= 3^{5\cdot 8}=(3^{5})^{8}=\boxed{\bf 243^{8}}[/tex]
[tex]\bf 2^{72}= 2^{9\cdot 8}=(2^{9})^{8}=\boxed{\bf 512^{8}}[/tex]
[tex]\bf \implies243^{8}<512^{8}\implies \boxed{ \boxed{\bf 3^{40}<2^{72}}}[/tex]
[tex]\it~~[/tex]
[tex]\bf d)~2^{43}= 2\cdot 2^{42}=2\cdot 2^{6\cdot 7}=2\cdot(2^{6})^{7}=\boxed{\bf 2\cdot 64^{7}}[/tex]
[tex]\bf ~7^{14}= 7^{2\cdot 7}=(7^{2})^{7}=\boxed{\bf 49^{7}}[/tex]
[tex]\bf \implies \boxed{ \boxed{\bf 2\cdot 64^{7}>49^{7}}}[/tex]
[tex]\it~~[/tex][tex]\bf e)~27^{100}= (3^{3})^{100}=3^{3\cdot 100}=3^{300}=3^{5\cdot 60}=(3^{5})^{60}=\boxed{\bf 243^{60}}[/tex]
[tex]\bf \implies \boxed{ \boxed{\bf 243^{60}>99^{60}}}[/tex]
P.S.: Daca esti pe telefon, te rog sa glisezi spre dreapta pentru a vedea rezolvarea completa
Bafta multa!
==pav38==
