Question

Determinați numărul natural x astfel incat:2 la puterea 1×2 la puterea2×2 la puterea 3×.....×2 la puterea 50=2 la puterea x

Answer 1

2 la puterea 1 •2 la puterea 2 • … •2 la puterea 50=2 la puterea 1+2+...+50=2 la puterea 50•51:2=2 la puterea 1275
Raspuns: x=1275

Answer 2

2^1 × 2^2 × 2^3 ×...× 2^50 = 2^x

2^(1+2+3+...+50) = 2^x

x = 1 + 2 + 3 +...+ 50

x = 50 × (50 + 1) : 2

x = 25 × 51

x = 1 275