Question 295638
    log(2x+6)+log(x-2)=2
    log(2x+6)(x-2)=2
    (2x+6)(x-2)= 10^2
    2x^2-4x+6x-12 = 100
    2x^2+2x-12 = 100
    x^2+x-6 = 50
    x^2+x-56 = 0
    (x+8)(x-7) = 0
.
x = {-8,7}
Trying to plug the answers above, we see that when x=-8:
log(x-2) = log(-8-2) = log (-10)
we can't take log of a negative number
so, -8 is an "extraneous" answer -- throw it out leaving
your solution as:
x = 7