SOLUTION: how do you solve this 2 log (x + 4 ) -log (x+2 ) = 3 + log (x - 2 ) 10 10 10 should is start of with the quotient rule or bring a

Click here to see ALL problems on logarithm

Question 750469: how do you solve this
2
log (x + 4 ) -log (x+2 ) = 3 + log (x - 2 )
10 10 10
should is start of with the quotient rule
or
bring all logs to one side first , take log (x-2) to the other side
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
log (x + 4 ) -log (x+2 ) = 3 + log (x - 2 )
10 10 10
------------------------
log[(x+4)/(x+2)]- log(x-2) = 3
----------------------------
log[(x+4)/((x+2)(x-2))] = 3
-------
log[(x+4)/(x^2-4)] = 3
------------------
(x+4)/(x^2-4) = 10^3 = 1000
-----
(x+4) = 1000x^2-4000
----
1000x^2 -x -4004 = 0
x = 2.0015
================
Cheers,
Stan H.

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
log(x^2 + 4) - log(x+2) = 3 + log(x - 2)
log(x^2 + 4) - log(x+2) = log(1000) + log(x - 2)
----
(x^2+4)/(x+2) = 1000(x-2)
x^2+4 = 1000(x^2-4) = 1000x^2 - 4000
999x^2 = 4004

x =~ 2.002
----------------
Ignore the negative value of x