Question

Determinati numarul natural x astfel incat:
d) (2 la puterea 3× 3 la puterea 5) la puterea 2 : (2 la puterea 4× 3 la puterea 6) : 3 la puterea 2=6 la puterea X
e) (4×8) la puterea 15 : 4 la puterea 5 : 2 la puterea 6=2 la puterea X
f) 2 la puterea 1 × 2 la puterea 2 × 2 la puterea 3.....×2 la puterea 50=2 la puterea X
Va rog, imi trebuie urgent pentru ca e pentru astazi!!!!! pls

Answer 1

d) (2 la puterea 3× 3 la puterea 5) la puterea 2 : (2 la puterea 4× 3 la puterea 6) : 3 la puterea 2=6 la puterea X
(2^6*3^10):(2^4*3^6):3^2=6^x
2^2*3^4:3^2=6^x
2^2*3^2=6^x
6^2=6^x => x=2

e) (4×8) la puterea 15 : 4 la puterea 5 : 2 la puterea 6=2 la puterea X
4^15*8^15:4^5:2^6=2^x
4^10*2^45:2^6=2^x
2^20*2^39=2^x
2^59=2^x => x=59

f) 2 la puterea 1 × 2 la puterea 2 × 2 la puterea 3.....×2 la puterea 50=2 la puterea X 
2^1*2^2*2^3*....*2^50=2^x => 2^1275=2^x => x=1275
1+2+3+...+50=1275