Question

Determinati numerele naturale n pentru care:
a) 8 la puterea n +8 la puterea n+1=18×2 la puterea 2003
b) 9 la puterea n + 9 la puterea n+1=10×3 la puterea 2012
c)6 la puterea n + 6 la puterea n+3= 217×6 la puterea 55


VA ROG SA MA AJUTATI

Answer 1

a) 8^n+8^n+1=18*2^2003
8^n(1+8)=9*2*2^2003
8^n*9=9*2^2004
2^3n=2^2004
3n=2004
n=668
b) 9^n+9^n+1=10*3^2012
9^n(1+9)=10*3^2012
9^n*10=10*3^2012
3^2n=3^2012
2n=2012
n=1006
c) 6^n+6^n+3=217*6^55
6^n(1+6^3)=217*6^55
6^n*217=217*6^55
n=55