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Question Number 63833 by gunawan last updated on 10/Jul/19

$$\mathrm{If}\mathrm{the}\mathrm{binomial}\mathrm{coefficients}\mathrm{of}2\mathrm{nd},3\mathrm{rd}$$$$\mathrm{and}4\mathrm{th}\mathrm{terms}\mathrm{in}\mathrm{the}\mathrm{expansion}\mathrm{of}$$$${[\sqrt{2^{{\log }_{10}(10-3^x)}}+\sqrt[5]{2^{(x-2){\log }_{10}3}}]}^m\mathrm{are}\mathrm{in}$$$$\mathrm{AP}\mathrm{and}\mathrm{the}6\mathrm{th}\mathrm{term}\mathrm{is}21,\mathrm{then}\mathrm{the}\mathrm{value}\left(\mathrm{s}\right)$$$$\mathrm{of}x\mathrm{is}\left(\mathrm{are}\right)$$

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