Question 306865
2ln(x)-ln((x+8)/3)= ln(6)
ln(x^2)-ln((x+8)/3)= ln(6)
ln(x^2)/((x+8)/3)= ln(6)
(x^2)/((x+8)/3)= 6
(x^2) = 6((x+8)/3)
(x^2) = 2(x+8)
(x^2) = 2x+16
x^2-2x-16 = 0
.
Solve by applying the quadratic formula.  Doing so yields:
x = {5.123, -3.123}
Toss out the negative solution (extraneous) leaving:
x = 5.123
.
Details of quadratic formula follows:
*[invoke quadratic "x", 1, -2, -16 ]