Question

Please help!

Solve the logarithmic equation algebraically.
ln(x + 9) = ln(x - 6) - ln(x + 6)

Answer 1

ln(x + 9) = ln(x - 6) - ln(x + 6) , but:

ln(x - 6) - ln(x + 6) = ln[(x-6)/(x+6)], So:

If ln(x + 9) = ln[(x-6)/(x+6)], then:

(x+9) = (x-6)/(x+6), Cross multiplication:

(x+9)(x+6) = (x-6) →→ x² + 14x + 60 = 0

Solving this quadratic equation gives :

x₁ = -7+√11 .i
x₂ = -7 -√11 .i