## College Algebra (10th Edition)

domain: $(0, +\infty)$
RECALL: The logarithmic function $f(x) = \log_a{x}$ is defined only when $x \gt 0$. Thus, its domain is $x \gt 0$. This means that the function $f(x) = \log_5{(x^3)}$ is defined only when $x^3 \gt 0$. Note that the value of $x^3$ will be greater than zero only when $x$ is positive. This means that the given function is defined only when $x\gt0$. Thus, the domain of the given function is $x\gt 0$. In interval notation, the domain is $(0, +\infty)$.