Răspuns:
Explicație pas cu pas:
La a) MVA se afla din conditia 2x-1>0, deci x>1/2
La b) MVA se afla din conditiile x>0 si x-1>0, deci x>0 si x>1, deci x>1.
[tex]a)~~log_{3}log_{2}(2x-1)=0, ~~log_{2}(2x-1)=3^{0},~~log_{2}(2x-1)=1,~~2x-1=2^{1},~~2x=2+1, ~~2x=3,~~x=\frac{3}{2}.\\b)~~log_{2}x+log_{2}(x-1)=1,~~log_{2}(x(x-1))=1,~~x(x-1)=2^{1}[/tex]
x²-x-2=0, Δ=1-4·1·(-2)=1+8=9>0, deci x1=(1-3)/2=-1 si x2=(1+3)/2=2
-1∉MVA, 2∈MVA. Deci S={2}.
