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Question Number 66396 by hmamarques1994@gmai.com last updated on 14/Aug/19

$$$$$$\mathbf{Seja}{53}^{{\mathbf{log}}_{\frac{1}{\sqrt{{\mathit{e}}^{\mathit{\pi }}}}}\left[\sqrt[9999999]{(\mathit{x}+11)!}\right]}=1.$$$$$$$$$$$$$$$$\mathbf{Calcule}\frac{{\mathbf{x}}_1}{{\mathbf{x}}_2}+0,9.$$

Answered by mr W last updated on 14/Aug/19

$${53}^{{\mathbf{log}}_{\frac{1}{\sqrt{{\mathit{e}}^{\mathit{\pi }}}}}\left[\sqrt[9999999]{(\mathit{x}+11)!}\right]}=1$$$$\Rightarrow {\mathbf{log}}_{\frac{1}{\sqrt{{\mathit{e}}^{\mathit{\pi }}}}}\left[\sqrt[9999999]{(\mathit{x}+11)!}\right]=0$$$$\Rightarrow \sqrt[9999999]{(\mathit{x}+11)!}=1$$$$\Rightarrow (x+11)!=1$$$$\Rightarrow x+11=0or1$$$$\Rightarrow x=-11or-10$$$$\Rightarrow x_1=-11,x_2=-10or{x}_1=-10,x_2=-11$$$$\Rightarrow \frac{x_1}{x_2}+0.9=\frac{11}{11}+\frac{9}{10}=2$$$$or$$$$\Rightarrow \frac{x_1}{x_2}+0.9=\frac{10}{11}+\frac{9}{10}=\frac{199}{110}$$

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