SOLUTION: solve the equation. log(x+2)= -log(x-1) +1

Question 185230: solve the equation. log(x+2)= -log(x-1) +1
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
solve the equation. log(x+2)= -log(x-1) +1
Assuming all are "common logs", base 10
log(x+2) + log(x-1) = 1
log((x+2)*(x-1)) = log(10)
(x+2)*(x-1) = 10
x^2 + x - 2 = 10
x^2 + x - 12 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=49 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3, -4. Here's your graph:

Ignore the -4
x = 3

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