SOLUTION: Hi Tutor, I am stuck on this problem. ln(x+2)-ln(4)=-ln x Do I take the ln of 2 and subtract the ln of 4? I don't know what else to do to solve thi1s. Thank you

Question 193260This question is from textbook Basic Technical Mathematics
: Hi Tutor,
I am stuck on this problem. ln(x+2)-ln(4)=-ln x
Do I take the ln of 2 and subtract the ln of 4? I don't know what else to do to solve thi1s.
Thank you
This question is from textbook Basic Technical Mathematics

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Apply log rules:
ln(x+2)-ln(4)=-ln x
ln(x+2)-ln(4)+ln x = 0
ln[(x+2)/(4)]+ln x = 0
ln[x(x+2)/(4)] = 0
x(x+2)/(4) = e^0
x(x+2)/(4) = 1
x(x+2) = 4
x^2 + 2x = 4
x^2 + 2x - 4 = 0
Solve using the quadratic equation. Doing so yields:
x = {1.236, -3.236}
.
We can throw out the negative solution, leaving:
x = 1.236
.
Details of quadratic to follow:

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=20 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.23606797749979, -3.23606797749979. Here's your graph:

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