3) log₂(-x²-2x+3) = log₂(x²+x-2) -x²-2x+3 = x²+x-2 -2x² - 3x + 5 = 0 Solving for x using the quadratic formula: x = (-(-3) ± √((-3)² - 4(-25)))/(2*-2) x = (3 ± √(9 + 40))/(-4) x = (3 ± √49)/(-4) x = (3 ± 7)/(-4) x = 10/-4 or x = -4/-4 x = -2.5 or x = 1.
1) log₃(x+2) = 3 - log₃(5x+4)
log₃(x+2) + log₃(5x+4) = 3
log₃((x+2)(5x+4)) = 3
(x+2)(5x+4) = 3³
5x² + 14x + 8 = 27
5x² + 14x - 19 = 0
Solving for x using the quadratic formula:
x = (-14 ± √(14² - 45(-19)))/(2*5)
x = (-14 ± √(196 + 380))/10
x = (-14 ± √576)/10
x = (-14 ± 24)/10
x = 10/10 or x = -38/10
x = 1 or x = -3.8
2) log₃(x+1) + log₃(x+3) = 1
log₃((x+1)(x+3)) = 1
(x+1)(x+3) = 3¹
x² + 4x + 3 = 3
x² + 4x = 0
x(x+4) = 0
x = 0 or x = -4
3) log₂(-x²-2x+3) = log₂(x²+x-2)
-x²-2x+3 = x²+x-2
-2x² - 3x + 5 = 0
Solving for x using the quadratic formula:
x = (-(-3) ± √((-3)² - 4(-25)))/(2*-2)
x = (3 ± √(9 + 40))/(-4)
x = (3 ± √49)/(-4)
x = (3 ± 7)/(-4)
x = 10/-4 or x = -4/-4
x = -2.5 or x = 1.