Question

Aflati numarul natural r din egalitatea 2 la pueterea 2002 + 4 la puterea 1001=2 la puterea r

Answer 1

Salut,

2²⁰⁰² + 4¹⁰⁰¹ = 2²⁰⁰² + (2²)¹⁰⁰¹ = 2²⁰⁰² + 2²⁰⁰² = 2·2²⁰⁰² = 2²⁰⁰³, deci r = 2003.

Green eyes.

Answer 2

2^2002 + 4^1001 = 2^r

2^2002 + (2^2)^1001 = 2^r

2^2002 + 2^2002 = 2^r

2 × 2^2002 = 2^r

2^2003 = 2^r

r = 2003