SOLUTION: I need help on a logarithm problem. I need to Solve for X. 2ln(x)-ln(x+8/3)= ln(6)

Question 306865: I need help on a logarithm problem.
I need to Solve for X.
2ln(x)-ln(x+8/3)= ln(6)
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=68 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5.12310562561766, -3.12310562561766. Here's your graph:

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