Question 972064
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