expand log subscript 9 (x(x^2 2))/(sqrt x^2-2)

\log_9\ \frac{x(x^2 + 2)}{\sqrt{x^2 - 2}}

Start by using the basics?

\log_c\ ab = \log_c\ a + \log_c\ b

\log_c\ \frac{a}{b} = \log_c\ a - \log_c\ b

What can you get from here?