Question

determinati numarul natural ''x'' din urmatoarele egalitati :
a) 2 la puterea x+1 * 3 la puterea x = 72
b) 5 la puterea x / 5 la puterea a 3 = 25
c) 4 la puterea x / 2 la puterea a 2 = 64
d) 3 la puterea 2x - 1 = 3 la puterea a 7
e) ( x -2 ) totul la a 4 = 9 la puterea a 2 
f) 18 la puterea x+2 / 2 la puterea a 5 = 3 la puterea a 10

Answer 1

a)2*2^x*3^x=72
6^x=72:2=36 ⇒ x=2
b) 5^(x-3)=25=5^2
⇒ x-3=2⇒ x=5
c) 4^x/2^2=2^2x/2^2=2^(2x-2)=64=2^6
⇒ 2x-2=6⇒ 2x=8⇒ x=4
d) ⇒ 2x-1=7
2x=8⇒ x=4
e) [(x-2)^2]=9^2
⇒ x-2=9⇒x=11
f) 18^x*18^2/32=3^10
18^x*(2*9)^2=32*3^10
18^x*2^2*3^4=32*3^10
Impart prin 4*3^4
18^x=8*3^6
18^x=2^3*3^6
18^x=6^3*3^3=18^3
⇒ x=3