Question Number 186867 by Mingma last updated on 11/Feb/23
Answered by aba last updated on 11/Feb/23
$${x}=−\mathrm{5} \\ $$$$\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}\right)^{−\mathrm{4}} =\left(\frac{\mathrm{5}}{\mathrm{4}}\right)^{\mathrm{4}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{4}} \\ $$
Commented by Mingma last updated on 11/Feb/23
Good!
Answered by aba last updated on 11/Feb/23
$$\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}+\mathrm{1}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{4}} \Rightarrow\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}+\mathrm{1}} =\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}\right)^{−\mathrm{5}+\mathrm{1}} \\ $$$$\Rightarrow{x}=−\mathrm{5}\: \\ $$
Commented by Mingma last updated on 11/Feb/23
Good!