How to solve these logarithmic equations:
1.) log3(x+6)-log3(x-2)=2 [with a base of 3]
2.) log8(x-6)+log8(x+6)=2 [with a base of 8]
Ans:
Remember that Log a - log b = log (a/b)
log a + log b = log (a*b)
Also, if loga(x) = n i.e. log x to base a = n, then x = a^n

1)
logx(x+6) - log3(x-2) = log3((x+6)/(x-2)) = 2
So 

Simplifying and bring like terms to one side,
 or


2)
log8(x-6)+log8(x+6)= log8((x - 6)*(x + 6)) = 2



x = 10 or x = -10

:)