SOLUTION: log6 (sqrt x) + log6 (sqrt 6x+5) = 1

Question 206898This question is from textbook Intermediate Algebra
: log6 (sqrt x) + log6 (sqrt 6x+5) = 1 This question is from textbook Intermediate Algebra

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
If this is whagt you meant:

.
Then, applying "log rules" we get:

Solving the above with the quadratic equation yields the following:
x = {2.068, -2.901}
We can toss out the negative solution leaving:
x = 2.068
.
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=889 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.06800858597926, -2.9013419193126. Here's your graph:

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