# What is the domain of the function g(x) = 3log2(x−1)+4 ?

$\left\{x : x \in R \mathmr{and} x > 1\right\}$
Since you cannot have a log to a result which is either negative or 0 (that is, you cannot raise a number to any exponent which gives a result $\le$ 0), we know that $x - 1 > 0$.
Hence, adding 1 to each side, the domain is $x > 1$ (and $x \in R$).