Question

3 la puterea 2xn-3 = 27 la puterea 7: 9 la puterea 2. 5 la puterea 3xn+1= 25 la puterea 11. n= necunoscuta, x = ori, : = impartit.

Answer 1

$a).3^2^n^-^3=27^7:9^2 \\ 3^2^n^-^3=(3^3)^7:(3^2)^2 \\ 3^2^n^-^3=3^2^1:3^4 \\ 3^2^n^-^3=3^2^1^-^4 \\ 3^2^n^-^3=3^1^7 \\ 2n-3=17 \\ 2n=17+3 \\ 2n=20 \\ n=20:2 \\ n=10$
$b).5^3^n^+^1=25^1^1 \\ 5^3^n^+^1=(5^2)^1^1 \\ 5^3^n^+^1=5^2^2 \\ 3n+1=22 \\ 3n=22-1 \\ 3n=21 \\ n=21:3 \\ n=7$