Răspuns:
c) n = 7
d) n = 13
e) n = 15
Explicație pas cu pas:
c) [tex]5^{3*n+1}[/tex] = [tex]25^{11}[/tex]
[tex]5^{3*n+1}[/tex] = [tex]5^{22}[/tex]
[tex]3*n+1[/tex] = 22
[tex] 3*n[/tex] = [tex]22-1[/tex]
[tex] 3*n[/tex] = [tex]21[/tex]
[tex]n[/tex] = [tex]21:3[/tex]
[tex]n[/tex] = [tex]7[/tex]
d) [tex]7^{n+1} :7^{4}[/tex] = ([tex]49^{2}[/tex])^3
[tex]7^{n-3}[/tex] = [tex]49^{8}[/tex]
[tex]7^{n-3}[/tex] = [tex]7^{16}[/tex]
n-3 = 16
n = 16 + 3
n = 19
e) [tex]10^{2*n+1}:5^{2*n+1}[/tex] = [tex]8^{9}[/tex]
[tex]2^{2n+1}*5^{2n+1}:5^{2n+1} = 2^{27}[/tex]
[tex]2^{2n+1} = 2^{27}[/tex]
2n + 1 = 27
2n = 27 - 1
2n = 26
n = 26 ÷ 2
n = 13
