Răspuns:
Explicație pas cu pas:
b)
[tex]8^{17} = (2^3)^{17} = 2^{3*17} = 2^{51}\\16^{12} =(2^4)^{12}= 2^{4*12} = 2^{48} < 2^{51}\\\\8^{17} > 16^{12}[/tex]
c)
[tex]3^{39}= (3^3)^{13} = 3^{3*13} = 3^{39}\\9^{20} =(3^2)^{20}=3^{2*20} = 3^{40} > 3^{39}\\27^{13} < 9^{20}[/tex]
d)
[tex]9^{13} =(3^2)^{13}=3^{2*13} = 3^{26} < 3^{27}\\3^{27} > 9^{13}[/tex]
e) fie numerele x si y asa incat:
[tex]2^{33} = 10^x[/tex]
[tex]3^{22} = 10^y[/tex]
Avem:
[tex]2^{33} = 10^x \\log(2^{33}) = log(10^x)\\33*log(2) = x*log(10)\\33*log(2) = x\\x=33*log(2)=33*0,3010=9,9339[/tex]
Si
[tex]3^{22} = 10^y \\log(3^{22}) = log(10^y)\\22*log(3) = y*log(10)\\22*log(2) = y\\y=22*log(3)=22*0,4771=10,4966[/tex]
[tex]10,4996 > 9,9339\\y > x\\10^y>10^x\\3^{22} > 2^ {33}[/tex]
