SOLUTION: log base 8 of (x) + log base 8 of (x+2)=3

Question 572953: log base 8 of (x) + log base 8 of (x+2)=3
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
log base 8 of (x) + log base 8 of (x+2)=3
log base 8 of (x)(x+2)=3
(x)(x+2)=8^3
x^2+2x=512
x^2+2x-512 = 0
applying the quadratic formula results in:
x = {21.65, -23.65}
the negative solution is extraneous, throw it out leaving:
x = 21.65
.
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=2052 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 21.6495033058122, -23.6495033058122. Here's your graph:

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