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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Question 147784: Find the domain of g(x)=ln(x+4)? I am not sure what to do for this question with the ln? Help?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
note: ln is a logarithm where ln%28x%29=log%28e%2C%28x%29%29



ln%28x%2B4%29 Start with the given expression

Remember you cannot take the natural log of zero or of a negative value. So that means the argument x%2B4 must be greater than zero (i.e. the argument must be positive)

x%2B4%3E0 Set the inner expression greater than zero

x%3E0-4Subtract 4 from both sides


x%3E-4 Combine like terms on the right side


So that means x must be greater than -4 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 y=ln%28x%2B4%29, we get
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+ln%28x%2B4%29%29+ notice how the graph never crosses the line x=-4. So this graphically verifies our answer.

and we can see that x must be greater than -4 in order to lie on the graph