Having wrapped up your work on the smaller projects, you are finally able to turn your attention to the project you are most excited about: research! Being one of Casey's projects, the files needed are password protected. Once again, you review the hint that Casey has left as a reminder of the password. Find an exact solution for
\[
\ln (5)+\ln \left(5 x^{2}-2\right)=\ln (159)
\]

If there is no solution, enter NA. If there are multiple solutions, they should be separated by semicolons (e.g. $2 ; 4 ; 6$ or $x+1 ; x-1$ ).
\[
x=
\]

Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using appropriate mathematical concepts to support your co-workers and supervisor.

Step 1 ：\(\ln (5)+\ln (5x^{2}-2)=\ln (159)\)

Step 2 ：Using the property of logarithms, \(\ln (5(5x^2 - 2)) = \ln (159)\)

Step 3 ：Equating the arguments, \(5(5x^2 - 2) = 159\)

Step 4 ：Solving for x, \(5x^2 - 2 = 159/5\)

Step 5 ：\(5x^2 = 159/5 + 2\)

Step 6 ：\(5x^2 = 31.8 + 2\)

Step 7 ：\(5x^2 = 33.8\)

Step 8 ：\(x^2 = 33.8/5\)

Step 9 ：\(x^2 = 6.76\)

Step 10 ：Taking the square root of both sides, \(x = \sqrt{6.76}\) or \(x = -\sqrt{6.76}\)

Step 11 ：Checking the solutions in the original equation, for x = 2.6: \(\ln (5)+\ln (5 (2.6)^{2}-2)=\ln (159)\)

Step 12 ：This is a true statement, so x = 2.6 is a valid solution.

Step 13 ：Checking the solutions in the original equation, for x = -2.6: \(\ln (5)+\ln (5 (-2.6)^{2}-2)=\ln (159)\)

Step 14 ：This is also a true statement, so x = -2.6 is a valid solution.

Step 15 ：\(\boxed{x = 2.6, x = -2.6}\)