conditii de existenta: x≥0
x-1≥0
folosesc formula [tex]log_{x}a+log_{x}b=log_{x}(a*b) [/tex]
log₂x(x-1)=log₂12
baza=2>1=> x(x-1)=12
x²-x-12=0
Δ=(-1)²-4*1*(-12)
Δ=1+48=49.
[tex] x1=\frac{1+7}{2} =4[/tex]
[tex]x2= \frac{1-7}{2}=-3 [/tex]
verific conditiile: 4≥0(adevarat),4-1≥0(adevarat)
-3≥0(fals),-3-1≥0(fals)
soolutie finala: x=4
