1. **State the problem:** We need to analyze the function $f(x) = \log_2(3x - 2)$ and find its range. 2. **Recall the domain rule for logarithms:** The argument of a logarithm must be positive. So, we require: $$3x - 2 > 0$$ 3. **Solve the domain inequality:** $$3x > 2$$ $$x > \frac{2}{3}$$ 4. **Domain:** The function is defined for all $x$ such that $x > \frac{2}{3}$. 5. **Range of logarithmic functions:** The logarithm function $\log_b(y)$, where $b > 1$, has a range of all real numbers $(-\infty, \infty)$. 6. **Apply to our function:** Since $3x - 2$ can take any positive value from $0$ to $\infty$ as $x$ goes from $\frac{2}{3}$ to $\infty$, the output $f(x)$ can take any real number. 7. **Conclusion:** The range of $f(x) = \log_2(3x - 2)$ is $(-\infty, \infty)$. **Final answer:** $$\text{Range} = (-\infty, \infty)$$