Question 386879: Please help! Find the exact value for the solution of the equation. Simplify the radical.
log(x^2+4)-log(x+2)=3+log(x-2) Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Find the exact value for the solution of the equation.
log(x^2+4)-log(x+2)=3+log(x-2)
log(x^2+4)-log(x+2)-log(x-2)=3
log(x^2+4)-(log(x+2)+log(x-2))=3
log(x^2+4)-log(x+2)(x-2)=3
log(x^2+4)-log(x^2-4)=3 (difference of 2 squares
log(x^2+4)/(x^2-4)=3
10^3=(x^2+4)/(x^2-4)
1000=x^2+4/x^2-4 (base 10 raised to the logarithm of the number is equal to the number, in this case the number is (x^2+4)/(x^2-4)
1000x^2-4000=x^2+4
999x^2=4004
x^2 =4004/999=4.008 (rounded)
x=2.002 or -2.002 (reject) logarithm > 0
ans:x=2.002
check: log(2.002^2+4)-log(2.002+2)=3+log(2.002-2)
log(8.008)-log(4.002)=3+log(.002)
.301=.301 (rounded to 3 decimal places)
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