7. (a) Given that $$3 \log _ { 3 } ( 2 x - 1 ) = 2 + \log _ { 3 } ( 14 x - 25 )$$ show that $$2 x ^ { 3 } - 3 x ^ { 2 } - 30 x + 56 = 0$$ (b) Show that - 4 is a root of this cubic equation.
(c) Hence, using algebra and showing each step of your working, solve $$3 \log _ { 3 } ( 2 x - 1 ) = 2 + \log _ { 3 } ( 14 x - 25 )$$