SOLUTION: log(14x+45)-log 7=log 2-log x

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Question 609079: log(14x+45)-log 7=log 2-log x
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
log(14x+45)-log 7=log 2-log x
log((14x+45)/7) = log 2-log x
log((14x+45)/7) = log(2/x)
(14x+45)/7 = 2/x
cross-multiply:
x(14x+45) = 7*2
14x^2+45x = 49
14x^2+45x-49 = 0
solving for x by using the quadratic formula yields:
x = {0.86, -4.1}
we can throw out the negative solution (extraneous) leaving:
x = 0.86
.
Details of quadratic formula:
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=4769 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.859212381517078, -4.07349809580279. Here's your graph:
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