The answer is
[tex]x = 5[/tex]
Solution:
[tex] log_{3}(2x - 1) = 2 \\ log_{3}(2x - 1) = 2 \: \: \: \: \: \: \: x > \frac{1}{2} \\ 2x - 1 = 3 {}^{2} \\ 2x - 1 = 9 \\ 2x = 9 + 1 \\ 2x = 10 \\ x = 5 \: \: \: \: \: \: \: \: \: \: \: x > \frac{1}{2} \\ x = 5[/tex]
