Remember that you cannot take the log of a negative number, regardless of the base. Also, you can take the logarithm of zero, since no number raised to a power can equal zero (although it come very close).
Therefore, (x+3), the number inside the logarithm, must be greater than zero.
x+3 > 0
x > -3
The domain is x > -3,
or (-3, ∞) in interval notation