Es.256 equazioni logaritmiche

C.E. 

{x > 0

{LOG(2,x)^2 - 1 ≠ 0

[x ≠ 1/2 ∧ x ≠ 2 ∧ x > 0]

posto: LOG(2,x) = t

1/(t^2 - 1) + 1/(t + 1) = 1/(1 - t)

1/(t^2 - 1) + 1/(t + 1) + 1/(t - 1) = 0

t^2 - 1 = (t + 1)·(t - 1) ≠ 0-----> t ≠ -1 ∧ t ≠ 1

(già detto)

1 + (t - 1) + (t + 1) = 0

2·t + 1 = 0

t = - 1/2

LOG(2,x) = - 1/2----> x = √2/2

(x = 2^(- 1/2))