Question

Va rog multtttttttttttttttttttttt​

Answer 1

4 log₂² x - 5log₂ x² + 4 = 0 , x apartine (0, infinit)

4(log₂ x )² - 5log₂ x² +4 = 0

folosind formula logₐ (b^c) = c * logₐ (|b|)  pt 5 log₂ x²

4log₂ (x)² - 5*2log₂ (|x|) + 4= 0

4log₂ (x)² - 10log₂ (x) + 4= 0 /:2

2 log₂(x²) - 5log₂ (x) + 2 =0

notez pe t = log₂(x)

2t² - 5 t +2 = 0, delta = 25-16 = 9

t1 = (5+3)/4 = 8/4 = 2

t2 = (5-3)/4 = 2/4= 1/2

din t = log₂x => t1 = log₂ (x) = 1/2  => x = V2

t2 = log₂(x) = 2 => x = 4

deci S={ V2, 4}