Answer
a) $t\gt1.5$
b) $-1\gt x\cup 1\lt x$
Work Step by Step
We know that the argument must be positive for both functions because we can not take the log of a non-positive number.
a) Hence the domain is:
$2t-3\gt0\\2t\gt3\\t\gt1.5$
b) Hence the domain is:
$x^2-1\gt0\\x^2\gt1$
Thus, we have the domain:
$-1\gt x\cup 1\lt x$