domain and range of f(x)=log5(x^3) step by step

1. Consider the function: f(x) = \log_5(x^3)
2. To determine the domain, we need the argument of the logarithm to be greater than zero: x^3 > 0
3. Since x^3 > 0 when x > 0 , the domain is: \text{Dominio: } x > 0
4. To determine the range, note that the function f(x) = \log_5(x^3) can take any real number value because as x^3 ranges over positive real numbers, \log_5(x^3) ranges over all real numbers.
5. Therefore, the range is: \text{Rango: } (-\infty, \infty)

**Answer:**
\text{Dominio: } x > 0
\text{Rango: } (-\infty, \infty)