The ninth term in the expansion of ${\left\{ {{3^{{{\log }_3}\sqrt {{{25}^{x - 1}} + 7} }} + {3^{ - 1/8{{\log }_3}\left( {{5^{x - 1}} + 1} \right)}}} \right\}^{10}}$ is equal to $180$, then $x$ is: ( x 1)

Question

The ninth term in the expansion of ${\left\{ {{3^{{{\log }_3}\sqrt {{{25}^{x - 1}} + 7} }} + {3^{ - 1/8{{\log }_3}\left( {{5^{x - 1}} + 1} \right)}}} \right\}^{10}}$ is equal to $180$, then $x$ is: ( x > 1)

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The ninth term in the expansion of \({\left\{ {{3^{{{\log }_3}\sqrt {{{25}^{x - 1}} + 7} }} + {3^{ - 1/8{{\log }_3}\left…

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