Question

Determinati nr nat x din fiecare caz .
5 lax +2 -2*5la x+1-12*5 la x =375
2 la x *3la x+1=108
3 lax +1*5 la x=675
3 la x +2 * 7 la x -3 la x *7 la x +1 =2940

Answer 1

5^(x +2) -2*5^(x+1)-12*5^x =375
5^(x +2) -2*5^(x+1)-12*5^x =3*5³
5^x * (5²-2*5-12)=3*5³
5^x * (25-10-12)=3*5³
5^x *3=3*5³
x=3

2^x *3^(x+1)=108
2^x *3^(x+1)=2² *3³
2^x *3^x *3=2² *3³
2^x *3^x =2² *3²
(2*3) ^x=(2*3)²
x=2


3^(x +1)*5^x=675
3^x * 3 *5^x=3³*5²
3^x *5^x=3² *5²
(3*5)^x =(3 *5)²
x=2

Answer 2

$a).5^{x+2}-2 \cdot 5^{x+1} -12 \cdot 5^x=375 \\ 5^x(5^2-2 \cdot 5-12 \cdot 1)=375 \\ 5^x(25-10-12)=375 \\ 5^x \cdot 3=375 \\ 5^x=375:3 \\ 5^x=125 \\ 5^x=5^3 \\ x=3$
$b).2^x \cdot 3^{x+1}=108 \\ 2^x \cdot 3^x \cdot 3=108 \\ 2^x \cdot 3^x=108:3 \\ 2^x \cdot 3^x=36 \\ 6^x=6^2 \\ x=2$
$c).3^{x+1} \cdot 5^x=675 \\ 3^x \cdot 3 \cdot 5^x=675 \\ 3^x \cdot 5^x=675:3 \\ 3^x \cdot 5^x=225 \\ 15^x=15^2 \\ x=2$