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Question Number 170520 by mr W last updated on 25/May/22

$$solveforx$$$${(1+\frac{1}{x})}^{x+1}={(1+\frac{1}{10})}^{10}$$

Commented by mr W last updated on 26/May/22

$$yes.showhowyougot?$$

Commented by cortano1 last updated on 25/May/22

$$x=-11?$$

Answered by robertocaesar last updated on 26/May/22

$${\left(\frac{x+1}{x}\right)}^{x+1}=....$$$${\left(\frac{x}{x+1}\right)}^{-(x+1)}=....$$$${(1-\frac{1}{x+1})}^{-(x+1)}=....$$$${(1+\frac{1}{-(x+1)})}^{-(x+1)}={(1+\frac{1}{10})}^{10}$$$$\Rightarrow x=-11$$

Commented by mr W last updated on 26/May/22

$$thanks!$$

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