SOLUTION: log(x + 3) = 1 - log(x - 2) Solve for x

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Question 919205: log(x + 3) = 1 - log(x - 2) Solve for x
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
log(x + 3) = 1 - log(x - 2)
log(x + 3) + log(x - 2) = 1

(x+3)(x-2) = 10
x^2 + x - 6 = 10
x^2 + x -16 = 0
x = 3.53112887414927
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=65 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3.53112887414927, -4.53112887414927. Here's your graph:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!




...........
if log same, then



.......use quadratic formula to solve for






solutions:





or





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