Question

Rezolvati in multimea numerelor reale ecuatia log in baza 2 x+log in baza (5-2x)=1

Answer 1

DVA: x>0
5-2x>0, -2x>-5, x<5/2
DVA=(0, 2,5).
log in baza 2 din x+log in baza 2 din(5-2x)= 1
 log in baza 2 din x(5-2x)= 1
5x-2x^2=2
-2x^2+5x-2=0
2x^2-5x+2=0
delta= 9
x1=5+3/4=2
x2=5-3/4=1/2
S={0,5;2}.