Example: What is the domain of the logarithmic function?
\[g(x) = \log_7\left(x^2-9\right)\]Solution
Whenever we consider a question about the domain of a logarithm, we should begin with the basic notion that the inner part of the logarithm must be positive. This allows us to write down an equality in order to solve for the domain: \[ \solve{ x^2-9 &\gt& 0\\ x^2&\gt& 9\\ x\lt -3&&x\gt3 } \]