To find the domain of the function $f(x) = \log_2(x + 5)$, we analyze the expression within the logarithm. The logarithm function is defined only for positive arguments, i.e., $x + 5 > 0$.

Step-by-Step Solution:

1. Solve the inequality for the argument: $x + 5 > 0$ Subtract $5$ from both sides: $x > -5$

2. This means the domain of $f(x)$ is all $x$ values greater than $-5$.

Final Answer:

$\text{Domain: } (-5, \infty)$

Would you like additional explanation or examples?

---

Related Questions:

1. What is the domain of $f(x) = \log_3(x - 7)$?
2. How would the domain change for $g(x) = \log_2(-x - 5)$?
3. What is the domain of $h(x) = \ln(x^2 - 4)$?
4. What happens if $f(x) = \log_2|x + 5|$?
5. Can $f(x) = \log(x + 5)$ have a domain with negative inputs?

---

Tip:

For logarithmic functions, always ensure the argument inside the logarithm is strictly positive before solving for the domain.