SOLUTION: solve the equation log(5x-1) + log(x+2)=1

Question 313667: solve the equation log(5x-1) + log(x+2)=1
Found 2 solutions by nerdybill, Fombitz:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
log(5x-1) + log(x+2)=1
log(5x-1)(x+2)=1
(5x-1)(x+2)=10^1
5x^2+10x-x-2 = 10
5x^2+9x-2 = 10
Use the quadratic formula to get our solutions:
x = {0.892, -2.692}
Checking for extraneous solutions we see that we can throw out the negative solution leaving:
x = 0.892
.
Details of quadratic follows:

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=321 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.891647286716892, -2.69164728671689. Here's your graph:

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Use the quadratic formula,

Only the positive solution will be considered since the log function requires non-negative arguments.
or approximately,

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