[tex]Domain:\\\\10x-1 > 0\ and\ 9x+7 > 0\\\\10x > 1\ and\ 9x > -7\\\\x > \dfrac{1}{10}\ and\ x > -\dfrac{7}{9}\Rightarrow x > \dfrac{1}{10}\\\\D=\left\{x|x > \dfrac{1}{10}\right\}\\\\\log_5(10x-1)=\log_5(9x+7)\iff10x-1=9x+7\qquad\text{add 1 to both sides}\\\\10x=9x+8\qquad\text{subtract 9x from both sides}\\\\x=8\in D\\\\Answer:\ \boxed{x=8}[/tex]
