Question

log3(x)+logx(3)=3
Срочно помогите,подробно

Answer 1

Решение
Log3(x)+logx(3)=3
x > 0, x ≠ 1
Log₃(x) + log₃ (3) / log₃ (x) = 3
log²₃ (x) - 3*log₃ (x) + 1 = 0
log₃ (x) = t
t² - 3t + 1 = 0
D = 9 - 4*1*1 = 5
t₁ = (3 - √5)/2
t₁ = (3 + √5)/2
log₃ (x) = (3 - √5)/2
x₁ = 3^((3 - √5)/2
x₂ = 3^((3 + √5)/2