Question 108376
The domain of the function is all values of x where the function is defined. 
In other words, look for where the function is undefined and the answer is everywhere other than that. 
First one: {{{g(x)=log((x+3))}}}
The log function is only defined when the argument is >0.
{{{x+3>0}}}
{{{x>-3}}}
The domain of g(x) is all x such that x>-3.
Second case : {{{g(t)=ln(t-1)}}} 
Similarly, the natural log is only defined when the argument is >0.
{{{t-1>0}}}
{{{t>1}}}
The domain of g(t) is all t such that t>1.