If, by that, you mean x positive, you are right. What makes you think you are wrong?
But, of course, the domain of ln(x) is not necessarily the same as the domain of ln(4+ ln(x)). In order to be able to take the second logarithm, you must have 4+ ln(x)> 0 or ln(x)> -4. For what value of x is ln(x)= -4?
You already know that. That's the wrong question!Can anyone explain how to find the domain of ln(x)?