Question

Aflati nr natural n pentru care 2^n ori 5^n-1 = 2000

Answer 1

2^n ori 5^n-1 = 2000

2^n-1 * 2 * 5^n-1 = 2000

10^n-1 = 1000 = 10^3

n-1 = 3

n = 4

Answer 2

2ⁿ x 5ⁿ⁻¹ = 2 000

2ⁿ x 5ⁿ x 5⁻¹ = 2 000

( 2 x 5 )ⁿ  x 1 / 5 = 2 000

10ⁿ = 2 000 : 1 / 5

10ⁿ = 2 000 x 5

10ⁿ = 10 000

10ⁿ = 10⁴ ⇒     n = 4