SOLUTION: Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) log(x + 3) = 1 − log(x − 2) Since the bases are the same I s

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Question 1156594: Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
log(x + 3) = 1 − log(x − 2)
Since the bases are the same I set them equal to each other and got x+3=1-x+2 and solved to get x=0 which is incorrect. What did I do wrong?
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
log(x + 3) = 1 − log(x − 2)
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Do NOT enter (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) What is the point of that?
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log(x + 3) = 1 − log(x − 2)

Assuming base 10:
log(x + 3) = log(10) − log(x − 2)
log(x+3) = log(10/(x-2))
x+3 = 10/(x-2)
x^2 + x - 6 = 10
x^2 + x - 16 = 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=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:

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The negative solution gives a negative argument for the log, ignore it.
x =~ 3.5311
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