Question 147784
note: ln is a logarithm where {{{ln(x)=log(e,(x))}}}




{{{ln(x+4)}}} 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+4}}} must be greater than zero (i.e. the argument <font size=4><b>must</b></font> be positive)


{{{x+4>0}}} Set the inner expression greater than zero


{{{x>0-4}}}Subtract 4 from both sides



{{{x>-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

*[Tex \LARGE \textrm{\left{x|x>-4\right}}]


So here is the domain in interval notation: *[Tex \LARGE \left(-4,\infty\right)]



Notice if we graph {{{y=ln(x+4)}}}, we get

{{{ graph( 500, 500, -10, 10, -10, 10, ln(x+4)) }}} 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