Question

Determinați numarul natural n pentru care are loc: 3 la puterea n-1 = 81 la puterea 2

Answer 1

$3^{n-1}=81^2$

$3^{n-1}=(3^4)^2$

$3^{n-1}=3^8$

$n-1=8$

$n=9$

Answer 2

3 la puterea n-1 = 81 la puterea 2

3ⁿ - 1  = 81² ⇔ 3ⁿ  = 81² +1 ⇔ log₃3ⁿ = log₃ 6562 ⇔ nlog₃3 = log₃ 6562 ⇔

⇔ n·1 =  log₃ 6562 ⇔ n = log₃ 6562