Question

Determinati numarul natural n stiiind ca: [(4/7-1/5)la puterea 4]la puterea n=[(13/35)la puterea 7]la puterea n ÷(13/25)totul la 12

Answer 1

Am rezolvat problema considerand ca ultima fractie este (13/25)^12, doar asa se poate rezolva:

[(4/7-1/5)^4]^n = [(13/35)^7]^n:(13/35)^12
(20/35 - 7/35)^4n = (13/35)^7n : (13/35)^12
(13/35)^4n = (13/35)^7n x (35/13)^12
(13/35)^4n = (13^7n/35^7n) x (35^12/13^12)
(13/35)4n = 13^(7n-12)/35^(7n-12)
(13/35)^4n = (13/35)^(7n-12)
4n = 7n-12
3n = 12
n = 4