Question

Va rog sa ma ajutati cu acest exercitii . Subpunctele b-f.

Answer 1

la b)
Conditie: 2x>0  x>0  x apartine (2, infinit)
log2 2x + logx 2x =4
log2 2x + log2 2 / log2 2x = 4
log2 2x + 1/log2 2x = 4
(log2 2x)^2 + 1 = 4 log2 2x
Notam log2 2x=t
t^2 - 4t +1 = 0
t1= 2+radical 3
t2 = 2-radical 3 
=> log2 2x1 = 2+radical 3
2x1 = 2 ^ (2+radical 3)
log2 2x2= 2-radical 3
2x2 = 2 ^ (2-radical 3)

x are valorile {2 ^ (2-radical3) ; 2^ (2+radical3) }