Răspuns:
[tex]\frac{2lgx}{lg(5x-4)}[/tex] = 1
C.E: 5x - 4 > 0 => 5x > -4 => x > [tex]\frac{-4}{5}[/tex] => x ∈ ( [tex]\frac{-4}{5}[/tex] , + ∝ )
2lgx = lg ( 5x - 4 )
lg x² = lg ( 5x - 4 )
5x - 4 = x²
x² - 5x + 4 = 0
Δ = b² - 4ac = 25 - 16 = 9
x₁ = ( -b + √Δ ) / 2a = ( 5 + 3 ) / 2 = 8 / 2 = 4
x₂ = ( -b - √Δ ) / 2a = ( 5 - 3 ) / 2 = 2 / 2 = 1
S = { 1, 4 } ∈ ( [tex]\frac{-4}{5}[/tex] , + ∝ )
