SOLUTION: Solve the logarithmic equation for x. (Round your answer to four decimal places.) ln(x − 6) + ln(x + 7) = 1

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Question 446447: Solve the logarithmic equation for x. (Round your answer to four decimal places.)
ln(x − 6) + ln(x + 7) = 1
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
ln(x − 6) + ln(x + 7) = 1
ln(x − 6)(x + 7) = 1
(x − 6)(x + 7) = e^1
x^2+x-42 = e^1
x^2+x-42-e^1 = 0
x^2+x-42-2.718282 = 0
x^2+x-44.718282 = 0
apply the quadratic formula to get:
x = {6.2058, -7.2058}
the negative solution is extraneous -- throw it out leaving:
x = 6.2058
.
Details of quadratic 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=179.87312732 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 6.20583938295572, -7.20583938295572. Here's your graph:
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