SOLUTION: Any help would be greatly appreciated on this equation: log(x+84)-log(x+9)=log(x)

Question 376640: Any help would be greatly appreciated on this equation: log(x+84)-log(x+9)=log(x)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
log(x+84)- log(x+9) = log(x)
:
Combine the 1st two logs, subtracting means divide
= log(x)
:
therefore
= x
:
x + 84 = x(x+9)
x + 84 = x^2 + 9x
0 = x^2 + 9x - x - 84
A quadratic equation
x^2 + 8x - 84 = 0
Factors to
(x+14)(x-6) = 0
Two solutions
x = -14*
and
x = 6
:
Checking solutions in original problem' only x = 6 can be a solution
:
log(6+84)- log(6+9) = log(6)
log(90)- log(15) = log(6)
1.954 - 1.176 = .778
.778 = .778
:
:
* the solution x=-14 would put a negative value in log(x+9)
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