Binomial Theorem

A possible value of 'x', for which the ninth term in the expansion of \({\left\{ {{3^{{{\log }_3}\sqrt {{{25}^{x - 1}} + 7} }} + {3^{\left( { - {1 \over 8}} \right){{\log }_3}({5^{x - 1}} + 1)}}} \right\}^{10}}\) in the increasing powers of \({3^{\left( { - {1 \over 8}} \right){{\log }_3}({5^{x - 1}} + 1)}}\) is equal to 180, is :