Question

Cum rezolv lg (x la a doua - 4x) = lg3 (2-x) ?

Answer 1

Conditia de existent a logaritmilor:
x²-4x>0, x(x-4)>0, x∈(-∞,0)U(4,+∞)
2-x>0, -x>-2, x<2 x∈(-∞,2)

x²-4x=3(2-x)
x²-4x=6-3x
x²-x-6=0
Δ=1-4x1x(-6)=1+24=25, √Δ=5
x1=(1+5)/2=3∉conditiilor de existent a logaritmilor
x2=(1-5)/2=-2∈(-∞,0) este solutia