A possible value of ' \(x\) ', for which the ninth term in the expansion of \(\left\{3^{\log _3 \sqrt{25^{x-1}+7}}+3^{\l…

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

[JEE Main 2021, 27 Jul (Shift 2)]