How to solve for log(base 3)6+log(base 3)6-log(base3)4

Use the fact that log(a) + log(b) = log(a*b)

and log(a) - log(b) = log(a/b) regardless of the base for the logarithm.

In this case you can rewrite the equation as:

log(base 3)[6*6/4] = log(base 3)[9] = 2 ( because you must raise 3 to the power of 2 in order to get 9)

log(base 3)6+log(base 3)6-log(base3)4 =
log(base3)(6*6/4) = log(3)9