Question

sa se determine x din: 3la x+3supra 9+3la x+5supra 27 +3la x +7supra 81 +3la x+9 supra243=1080

Answer 1

3^(x+3)/9+3^(x+5)/27+3^(x+7)/81+3^(x+9)/243=1080
27×3^(x+3)+9×3^(x+5)+3×3^(x+7)+3^(x+9)=1080×243
3^(x+3)×(27×3^0+9×3^2+3×3^4+3^6)=1080×243
3^(x+3)×(27+81+243+729)=1080×243
3^(x+3)×1080=1080×243
3^(x+3)=243
3^(x+3)=3^5
x+3=5
x=2