Question 1005768
Some help to start:
{{{x+sqrt(x^2-9)>0}}} and {{{sqrt(x^2-9)>=0}}}; The square root also requires  {{{x>=3}}}, the most important part of establishing the domain.


If you could use graphing device to avoid the algebra, then  
{{{graph(300,300,-6,6,-10,10,ln(x+sqrt(x^2-9)))}}}