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Question Number 32446 by Mr eaay last updated on 25/Mar/18

Answered by MJS last updated on 25/Mar/18

$$\mathrm{left}\mathrm{side}:$$$$8^{\frac{(x-1)x^{2x}}{x^x(x-2)}}\times {16}^{x^x}=8^{\frac{(x-1)x^x}{x-2}}\times 8^{\frac{4x^x}{3}}=$$$$=8^{(\frac{1}{x-2}+\frac{7}{3})x^x}=2^{(\frac{3}{x-2}+7)x^x}$$$${64}^{\frac{x\times x^{2x}}{x^x\times x^x}}={64}^x=2^{6x}$$$$\mathrm{left}\mathrm{side}=2^{(\frac{3}{x-2}+7)x^x-6x}$$$$$$$$\mathrm{right}\mathrm{side}:$$$${32}^{\frac{3(x-1)x^x}{x^{2x}}}={32}^{\frac{3(x-1)}{x^x}}=2^{\frac{15(x-1)}{x^x}}$$$$$$$$(\frac{3}{x-2}+7)x^x-6x=\frac{15(x-1)}{x^x}$$$$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{think}\mathrm{this}\mathrm{can}\mathrm{be}\mathrm{solved}$$$$\mathrm{exactly}.\mathrm{By}\mathrm{trying}\mathrm{I}\mathrm{found}$$$$x\approx .90597422346646$$

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