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Question Number 63935 by gunawan last updated on 11/Jul/19

$$\mathrm{If}\mathrm{the}{9}^{\mathrm{th}}\mathrm{term}\mathrm{in}\mathrm{the}\mathrm{expansion}\mathrm{of}$$$${[3^{{\log }_3\sqrt{{25}^{x-1}+7}}+3^{-\frac{1}{8}{\log }_3(5^{x-1}+1)}]}^{10}\mathrm{is}$$$$\mathrm{equal}\mathrm{to}180\mathrm{and}x>1,\mathrm{then}x\mathrm{equals}$$

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