Question

Determinati numarul natural n pentru care au loc egalitatile:
a)3^2*n-3=27^7:9^2
b)5^3*n+1=25^11
c)7^n+1:7^4=49^2^3
d)10^2*n+1:5^2*n+1=8^9
Ajutor!!!

Answer 1

a)3^2*n-3=27⁷:9²
3^2*n-3=(3³)⁷:(3²)²
3^2*n-3=3²¹:3⁴
3^2*n-3=3¹⁷
2n-3=17
2n=20
n=10

b)5^(3*n+1)=25¹¹
5^(3*n+1)=(5²)¹¹
5^(3*n+1)=5²²
3n+1=22
3n=21
n=7

c)7^(n+1):7⁴=(49²)³
7^(n+1-4)=(7⁴)³
7^(n-3)=7¹²
n-3=12
n=15

d)10^(2*n+1):5^(2*n+1)=8⁹
10^(2*n+1):5^(2*n+1)=(2³)⁹
2^(2*n+1)=2²⁷
2n+1=27
2n=26
n=13