Question

Determinati nr natural x astfel incat: A) (5 la puterea 12 : 5 la puterea 10- 4 la puterea 18 : 4 la puterea 16) : 3 la puterea 2 = x B) [ 2 la puterea 5 * (2*3) la puterea 7 ] : 3 la puterea 7 = 2 la puterea x C) ( 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 D) ( 4*8) la puterea 15 : 4 la puterea 5 : 2 la puterea 6 = 2 la puterea x E) 2 la puterea 1 * 2 la puterea 2 * 2 la puterea 3 * .......* 2 la puterea 50 = 2 la puterea x Va rog mult!! Dau coroana!!!!!

Answer 1

A) 5^12:5^10-4^18:4^16:3^2
5^12:5^10=5^2
4^18:4^16=4^2
3^2=3^2
5^2-4^2-3^2=25-16-9=0

B) 2^5*(2*3)^7:3^7=2^x
2^5*6^7:3^7=2^x
2^5*2^7=2^x
2^12=2^x
x=12

C) (2^3*3^5)^2:(2^4*3^6):3^2=6^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

D) (4*8)^15:4^5:2^6=2^x
(4*2*4)^15:4^5:2^6=2^x
4*2*4^10:2^6=2^x
2^2*2*(2^2)^10:2^6=2^x
2^23:2^6=2^x
2^17=2^x
17=x
x=17

E) 2^1*2^2*2^3*...2^50=2^x
1+2+3+....+50=x
suma Gauss
n(n+1)/2 unde n= 50
50*51/2=x
2550/2=x
1275=x
x=1275