Use the one-to-one property of logarithms to solve. \[ \ln \left(x^{2}-2\right)+\ln (9)=\ln (7) \] Enter the exact answers. The field below accepts a list of numbers or formulas separated by semicolons (e.g. $2 ; 4 ; 6$ or $x+1 ; x-1)$ \[ x= \] Show your work and explain, in your own words, how you arrived at your answer.

Step 1 ：\(\ln ((x^{2}-2) \cdot 9)=\ln (7)\)

Step 2 ：\(\ln (9x^{2}-18)=\ln (7)\)

Step 3 ：\(9x^{2}-18=7\)

Step 4 ：\(9x^{2}=25\)

Step 5 ：\(x^{2}=\frac{25}{9}\)

Step 6 ：\(x=\pm \sqrt{\frac{25}{9}}\)

Step 7 ：\(x=\pm \frac{5}{3}\)

Step 8 ：Check the solutions: For \(x=\frac{5}{3}\), \(x^{2}-2=\left(\frac{5}{3}\right)^{2}-2=\frac{7}{9}\), which is positive. For \(x=-\frac{5}{3}\), \(x^{2}-2=\left(-\frac{5}{3}\right)^{2}-2=\frac{7}{9}\), which is also positive.

Step 9 ：\(\boxed{x=\frac{5}{3}, x=-\frac{5}{3}}\)