Question

Given y = log3(x + 4), what is the domain?

Answer 1

The logaritm of b base a

$log_ab$

Conditions for the base a: $a>0 \ and \ a\ne 1$ 
Conditions for the number b: $b>0$

$b=x+4\\\\ x+4>0 \Rightarrow x>-4$

Answer
$D: \ x\in (-4;\infty)$ 

Answer 2

For a logarithmic function, we have a restriction on the domain.
Since log(0) isn't defined, we say that there is an asymptote at x = 0.
Thus, for the regular logarithmic function y = log(x), x > 0.

We can then say (x + 4) > 0, since that's when the function of a logarithm is defined as.
x + 4 > 0
x > -4

Thus, the domain of the logarithmic function is x > -4, where x is a real integer.