To find the domain of the function \( h(x) = \log_3(x - 3) \), we need to determine for which values of \( x \) the logarithm is defined.
The logarithmic function \( \log_b(y) \) is defined only for \( y > 0 \). Thus, for the function \( h(x) \) to be defined, we need:
\[ x - 3 > 0 \]
Solving this inequality gives:
\[ x > 3 \]
Therefore, the domain of \( h \) is all \( x \) such that \( x \) is greater than 3. In interval notation, this is:
\[ (3, \infty) \]
So, the domain of \( h \) is \( (3, \infty) \).