SOLUTION: How to solve for X: Log(base3) (x-4) = 2 - log(base3) (x+4) Answer given is "x=5" Could you please explain how to arrive at 5? Thank you, Tiffany

Question 972064: How to solve for X: Log(base3) (x-4) = 2 - log(base3) (x+4) Answer given is "x=5" Could you please explain how to arrive at 5?
Thank you,
Tiffany
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Log(base3) (x-4) = 2 - log(base3) (x+4)
log 3 (x-4) + log 3(x+4) =2
log 3{ (x-4)*(x+4)}=2 When you add logs, it is multiplication if you combine them with the same base.
log 10 (100) + log 10 (10)= log 10 (1000)=3 The left side is 2+1=3
Raise both to the 3 power. The log goes away.
(x-4)*(x+4)=9
x^2-16=9
x^2=25
x+ +5 -5 is extraneous.
Check log 3 (1)=2 - log 3 (9)
The left side is 0 (3^0=1)
The right side is 2-2=0
Checks

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