Given y=log3 (x+4) what is the domain

As you know, the domain is the values "x" can safely take on.

well, for a logarithmic expression, it can never have an expression of 0, namely in this case, x + 4 must never be 0, since such a logarithm doesn't exist.

now, x + 4 = 0 - - - > x = - 4.

thus if "x" ever becomes - 4, we'd end up with log₃ (-4+4), or log₃ (0), which is a no dice.

so the domain is all values except - 4.