Answer:
x = (7 + √133) / 6
Step-by-step explanation:
0 = log₉ (3x + 2) + log₉ (x − 3)
Use log rules:
0 = log₉ ((3x + 2) (x − 3))
Raise 9 to both sides:
1 = (3x + 2) (x − 3)
Simplify:
1 = 3x² − 7x − 6
0 = 3x² − 7x − 7
Use quadratic formula:
x = [ -(-7) ± √((-7)² − 4(3)(-7)) ] / 2(3)
x = (7 ± √133) / 6
Since x > 3:
x = (7 + √133) / 6
x ≈ 3.089
