SOLUTION: Find the domain of g(x)=ln(x+4)? I am not sure what to do for this question with the ln? Help?

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note: ln is a logarithm where



Start with the given expression

Remember you cannot take the natural log of zero or of a negative value. So that means the argument must be greater than zero (i.e. the argument must be positive)

Set the inner expression greater than zero

Subtract 4 from both sides


Combine like terms on the right side


So that means x must be greater than in order for x to be in the domain

So the domain in set-builder notation is


So here is the domain in interval notation:


Notice if we graph , we get
notice how the graph never crosses the line . So this graphically verifies our answer.

and we can see that x must be greater than in order to lie on the graph