\({3^{{{\log }_9}\left( {5x-5} \right)}} = 5.\)
ОДЗ: \(5x-5 > 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x > 1\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x\, \in \,\left( {1;\infty } \right).\)
\({3^{{{\log }_9}\left( {5x-5} \right)}} = 5\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{3^{{{\log }_{{3^2}}}\left( {5x-5} \right)}} = 5\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{3^{\frac{1}{2}{{\log }_3}\left( {5x-5} \right)}} = 5\,\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,\,{3^{{{\log }_3}\sqrt {5x-5} }} = 5\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\sqrt {5x-5} = 5\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,5x-5 = 25\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x = 6.\)
Ответ: 6.