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Question 64

A possible value of $$x$$, for which the ninth term in the expansion of $$\left\{3^{\log_3 \sqrt{25^{x-1}+7}} + 3^{\left(-\frac{1}{5}\right)\log_3(5^{x-1}+1)}\right\}^{10}$$ in the increasing powers of $$3^{\left(-\frac{1}{5}\right)\log_3(5^{x-1}+1)}$$ is equal to 180, is:

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