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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 14x%5E2%2B45x%2B-49+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2845%29%5E2-4%2A14%2A-49=4769.

Discriminant d=4769 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-45%2B-sqrt%28+4769+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2845%29%2Bsqrt%28+4769+%29%29%2F2%5C14+=+0.859212381517078
x%5B2%5D+=+%28-%2845%29-sqrt%28+4769+%29%29%2F2%5C14+=+-4.07349809580279

Quadratic expression 14x%5E2%2B45x%2B-49 can be factored:
14x%5E2%2B45x%2B-49+=+14%28x-0.859212381517078%29%2A%28x--4.07349809580279%29
Again, the answer is: 0.859212381517078, -4.07349809580279. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+14%2Ax%5E2%2B45%2Ax%2B-49+%29