# Chapter 4, Exponential and Logarithmic Functions - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 388: 75

Domain: $(-\infty,\ -1)\cup (1,\ \infty)$.

#### Work Step by Step

We need to find the domain of the given function: $g(x)=\log_{3}(x^{2}-1)$ We know that we can't take the log of a negative number, so: $x^{2}-1\gt 0$ $x^{2}\gt 1$ $x\lt -1$ or $x\gt 1$ Thus the domain is: $(-\infty,\ -1)\cup (1,\ \infty)$.

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