Question

Find the zero or zeroes of the function. Please help! :((

Answer 1

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