SOLUTION: log(2x+6)+log(x-2)=2
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Question 295638: log(2x+6)+log(x-2)=2
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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
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