Răspuns:
1. log₂ ( x - 3 ) = 0
C.E.: x - 3 > 0 => x > 3 => x ∈ ( 3, +∝ )
log₂ ( x - 3 ) = log₂ 1
x - 3 = 1
x = 4
2. log₅(9-x²) = 1
C.E.: 9 - x² > 0 => -x² > -9 => x² < 9 => x < 3 => x ∈ ( -∝, 3 )
log₅ ( 9 - x² ) = log₅ 5
9 - x² = 5
-x² = -4
x² = 4 => x = ± 2 => x = { -2, 2 } ∈ ( -∝, 3 )
3. log ₓ₊₂ 16 = 2
C.E.: x+2 > 0, x+2 ≠ 1
x > -2 => x ∈ ( -2, +∝ )
log ₓ₊₂ 16 = log ₓ₊₂ ( x + 2 )²
( x + 2 ) ² = 16
x² + 4x + 4 = 16
x² + 4x - 12 = 0
Δ = b² - 4ac = 16 + 48
Δ = 64
x₁ = ( -b + √Δ ) / 2a = ( -4 + 8 ) / 2 = 2 ∈ ( -2, +∝ )
x₂ = ( -b - √Δ ) / 2a = ( -4 - 8 ) / 2 = -6 ∉ ( -2, +∝ )
=> S = { 2 }
4. lg ( 3x - 8 ) = 2
C.E.: 3x - 8 > 0 => 3x > 8 => x > [tex]\frac{8}{3}[/tex] => x ∈ ( [tex]\frac{8}{3}[/tex] , +∝ )
lg ( 3x - 8 ) = lg 10²
3x - 8 = 100
3x = 108
x = 36
