Question

determinaţi numărul natural n pentru care au loc egalitatile: totul pe poza!ex16

Answer 1

b)
[tex]3^{2*n-3}=27^7:9^2 \\ \\ 3^{2n-3}=(3^3)^7:(3^2)^2 \\ \\ 3^{2n-3}=3^{3*7}:3^{2*2} \\ \\ 3^{2n-3}=3^{21}:3^4 \\ \\ 3^{2n-3}=3^{21-4} \\ \\ 3^{2n-3}=3^{17} \\ \\ 2n-3=17 \\ \\ 2n=17+3 \\ \\ 2n=20 \\ \\ n=10[/tex]

c)
[tex]5^{3n+1}=25^{11} \\ \\ 5^{3n+1}=(5^2)^{11} \\ \\ 5^{3n+1}=5^{22} \\ \\ 3n+1=22 \\ \\ 3n=21 \\ \\ n=7[/tex]

d)
[tex]7^{n+1}:7^4=49^{2^3} \\ \\ 7^{n+1-4}=(7^2)^{2*2*2} \\ \\ 7^{n-3}=(7^2)^8 \\ \\ 7^{n-3}=7^{16} \\ \\ n-3=16 \\ \\ n=13[/tex]

e)
[tex]10^{2n+1}:5^{2n+1}=8^9 \\ \\ (5*2)^{2n+1}:5^{2n+1}=8^9 \\ \\ 5^{2n+1}*2^{2n+1}:5^{2n+1}=8^9 \\ \\ 2^{2n+1}=8^9 \\ \\ 2^{2n+1}=(2^3)^9 \\ \\ 2^{2n+1}=2^{27} \\ \\ 2n+1=27 \\ \\ 2n=26 \\ \\ n=13[/tex]