SOLUTION: Find the exact value for the solution of the equation. log((x^2)+4)-log(x+2)=2+log(x-2) I have the answer in the back of my book and it says the answer is: (2/3)*(sqrt(101/11))=~

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Question 691108: Find the exact value for the solution of the equation.
log((x^2)+4)-log(x+2)=2+log(x-2)
I have the answer in the back of my book and it says the answer is: (2/3)*(sqrt(101/11))=~2.02
But every way I've tried didnt work. Please help! and thank you!

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
exact value for the solution of the equation.
log(x^2+4)-log(x+2) = 2+log(x-2)
subtracting indicates divide so we can write it
= 2 + log(x-2)
Subtract log(x-2) from both sides
- log(x-2) = 2
which we can combine
= 2
which is
= 2
find the antilog (10^x) of both sides (10^2 = 100)
= 100
multiply both sides by x^2-4


combine like terms
0 = 100x^2 - x^2 - 400 - 4
99x^2 - 404 = 0
99x^2 = 404
x^2 =
x =
x =
Extract the square roots of the perfect squares
x =*
x ~ 2.02

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