Question 143173
To find the domain of these, remember that you can't have a log of a negative, and you can't have a log of zero.  So, anything that is inside a logarithmic expression must be greater than zero.  In math symbols, this means that 
if you have log (x), then x>0.


In your case, you have g(x)=log(x+3) and g(t)=In(t-1).


Therefore, in the first function, x+3>0, so x>-3.  Interval notation: (-3, inf)
In the ssecond function, t-1 > 0, so t>1.  Interval notation:  (1, inf)


R^2